{"id":50441,"date":"2021-06-11T16:52:23","date_gmt":"2021-06-11T15:52:23","guid":{"rendered":"https:\/\/blogs.bmj.com\/bmj\/?p=50441"},"modified":"2021-06-18T21:20:54","modified_gmt":"2021-06-18T20:20:54","slug":"jeffrey-aronson-when-i-use-a-word-black-swans-in-microbiology","status":"publish","type":"post","link":"https:\/\/blogs.bmj.com\/bmj\/2021\/06\/11\/jeffrey-aronson-when-i-use-a-word-black-swans-in-microbiology\/","title":{"rendered":"Jeffrey Aronson: When I Use a Word . . . Black swans in microbiology"},"content":{"rendered":"<p><span style=\"font-weight: 400\">Continuing my search for biomedical black swans, based on the words newly cited in the <\/span><i><span style=\"font-weight: 400\">Oxford English Dictionary<\/span><\/i><span style=\"font-weight: 400\"> (<\/span><i><span style=\"font-weight: 400\">OED<\/span><\/i><span style=\"font-weight: 400\">) from 1970 to 2020, I now turn to terms relevant to microbiology and infectious diseases. Of 90 terms I\u2019ve surveyed, 52% describe viruses and viral diseases and 18% bacteria and bacterial diseases. The names of the bacteria are derived about equally from Latin and Greek words, whereas about one third of the names of the viruses are purely Latin in origin, and about one quarter are abbreviations; seven have combined Latin and Greek origins and seven are toponyms (Table 1).<\/span><\/p>\n<p><b>Table 1.<\/b><span style=\"font-weight: 400\"> Toponymic viruses, named since 1970<\/span><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-50442\" src=\"https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021.jpg\" alt=\"\" width=\"676\" height=\"327\" srcset=\"https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021.jpg 676w, https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021-300x145.jpg 300w, https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021-640x310.jpg 640w\" sizes=\"auto, (max-width: 676px) 100vw, 676px\" \/><\/p>\n<p><span style=\"font-weight: 400\">Toponymic nomenclature of infections and infectious organisms has been criticized recently, because of pejorative or accusatory uses, as if the rise of the infection was the fault of those who live in the area after which the causative organism was named. Toponymic infections include Bornholm disease and Marburg disease, but the best known is the Spanish flu, the 1918\u201320 influenza pandemic. It was so called, not because it was first observed in Spain, which is the usual toponymic justification, but because, in the absence of war-time press censorship, the Spanish newspapers provided extensive coverage of the pandemic.\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400\">Now the variant of SARS-CoV2 previously called the Indian variant, also known less memorably as B.1.617.2, is to be called the delta variant, to avoid any implication that India was responsible for it. The Greek alphabet has 24 characters, from alpha to omega, but there are three others, present in early scripts but obsolete in Attic times, known collectively as episema (singular episemon)\u2014a word that surprisingly has not made it into the <\/span><i><span style=\"font-weight: 400\">OED<\/span><\/i><span style=\"font-weight: 400\">. The letters were called digamma, koppa, and san or sampi, and they were retained in Attic Greek to symbolize numerals, since 27 letters are needed to cover all the integers from 1 to 999 (Table 2).<\/span><\/p>\n<p><b>Table 2.<\/b><span style=\"font-weight: 400\"> The 27 letters of the Greek alphabet used to represent numerals<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-50443\" src=\"https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021_2.jpg\" alt=\"\" width=\"602\" height=\"428\" srcset=\"https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021_2.jpg 602w, https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021_2-300x213.jpg 300w\" sizes=\"auto, (max-width: 602px) 100vw, 602px\" \/><\/p>\n<p><span style=\"font-weight: 400\">The digamma, which sounded like a vee or ef, can be seen in some Latin words that came from Greek before the digamma was dropped. Take the Attic Greek word for a ship, \u03bd\u03b1\u1fe6\u03c2 (naus), from which we get nautical; in Latin it was navis, which gives us navigate. The Greek word for a key was <\/span><i><span style=\"font-weight: 400\">\u03ba\u03bb\u03b5\u03af\u03c2<\/span><\/i> <span style=\"font-weight: 400\">(kleis), from which we get the musical instrument the ophicleide; in Latin it was clavis, which gives us a different instrument, the clavichord. In Greek, wine was <\/span><span style=\"font-weight: 400\">\u03bf\u1f36\u03bd\u03bf\u03c2 (<\/span><span style=\"font-weight: 400\">oinos), but in Latin vinum, giving us wine, vine, vinegar, viniculture, vintage, and vinyl\u2014the radical isomeric with ethenyl. In all these cases Latin retained the digamma, converting it to a vee.<\/span><\/p>\n<p><span style=\"font-weight: 400\">The episema are unlikely to be harnessed to designate the 25<\/span><span style=\"font-weight: 400\">th<\/span><span style=\"font-weight: 400\"> to 27<\/span><span style=\"font-weight: 400\">th<\/span><span style=\"font-weight: 400\"> variants of SARS-CoV2, when they emerge. Perhaps Oxford\u2019s way of grading students\u2019 work will prove useful, with marks such as alpha, beta-plus, and, for finer distinctions, alpha-beta-double-plus-minus.<\/span><\/p>\n<p><span style=\"font-weight: 400\">So what about the microbiological black swans? The antibiotic action of penicillin undoubtedly qualifies. But its isolation from a <\/span><i><span style=\"font-weight: 400\">Penicillium <\/span><\/i><span style=\"font-weight: 400\">mould by <\/span><a href=\"https:\/\/www.phc.ox.ac.uk\/news\/blog\/penicillin-in-oxford-four-plaques-and-a-memorial\"><span style=\"font-weight: 400\">Florey. Chain, and Heatley<\/span><\/a><span style=\"font-weight: 400\"> was a planned effort, and thereafter antibacterial drugs were specifically sought, starting with the <\/span><i><span style=\"font-weight: 400\">Actinomycetes<\/span><\/i><span style=\"font-weight: 400\">, soil organisms in which <\/span><a href=\"https:\/\/pubmed.ncbi.nlm.nih.gov\/24162573\/\"><span style=\"font-weight: 400\">Selman Waksman<\/span><\/a><span style=\"font-weight: 400\"> discovered streptomycin and from which many other antibacterial agents were later isolated.<\/span><\/p>\n<p><span style=\"font-weight: 400\">The death on 16 April of the pharmacologist <\/span><a href=\"https:\/\/www.dignitymemorial.com\/obituaries\/ann-arbor-mi\/ronald-cresswell-10158034\"><span style=\"font-weight: 400\">Ronnie Cresswell<\/span><\/a><span style=\"font-weight: 400\"> also reminds us of the discovery of azidothymidine (AZT), later called zidovudine, the first effective specific treatment for HIV AIDS. It had been synthesized in 1964 by <\/span><a href=\"https:\/\/pubmed.ncbi.nlm.nih.gov\/2661483\/\"><span style=\"font-weight: 400\">Jerome Horwitz<\/span><\/a><span style=\"font-weight: 400\"> at the Michigan Cancer Foundation, who had hoped to use it as an antimetabolite in leukaemia. It didn\u2019t prove useful, but in 1974 <\/span><a href=\"https:\/\/pubmed.ncbi.nlm.nih.gov\/2067571\/\"><span style=\"font-weight: 400\">Wolfram Ostertag<\/span><\/a><span style=\"font-weight: 400\"> in the Max Planck Institute in G\u00f6ttingen showed that it inhibited replication of a leukaemia retrovirus. So when Cresswell, leading drug development at Burroughs Wellcome, wanted to find a drug to inhibit the growth of HIV in vitro, his colleagues screened a range of compounds against other retroviruses, and there was <\/span><a href=\"https:\/\/scc-csc.lexum.com\/scc-csc\/scc-csc\/en\/item\/2020\/index.do\"><span style=\"font-weight: 400\">AZT<\/span><\/a><span style=\"font-weight: 400\">. A nucleoside chemist at Wellcome, Jane Rideout, chose it as one of a range of 14 different compounds, and her virologist colleague, Martha St Clair, did the screening. If that was a black swan, it took a long time to come out of hiding. Perhaps we can regard it as dark grey.<\/span><\/p>\n<p><span style=\"font-weight: 400\">Infections are not black swans, in the sense of discoveries that are made unexpectedly. Rather they discover us, as it were, not we them. It is as if the black swan has suddenly decided to show itself. Perhaps we should call them ugly ducklings.<\/span><\/p>\n<p style=\"text-align: left\"><span style=\"font-weight: 400\"><em><strong>Jeffrey Aronson<\/strong>\u00a0is a clinical pharmacologist, working in the Centre for Evidence Based Medicine in Oxford&#8217;s Nuffield Department of Primary Care Health Sciences. He is also president emeritus of the British Pharmacological Society.<\/em><\/span><\/p>\n<p style=\"text-align: left\"><strong>Competing interests:<\/strong> none declared.<\/p>\n<table>\n<tbody>\n<tr style=\"border: 1px solid black\">\n<td style=\"border: 1px solid black\">\n<p style=\"text-align: center\"><b>This week&#8217;s interesting integer: 326<\/b><\/p>\n<p style=\"text-align: center\"><b>Foyle\u2019s triangle<\/b><\/p>\n<ul>\n<li><span style=\"font-weight: 400\">Write down all the integers one after the other starting with 1 on its own, followed by 2 and 3 in the row below it, then 4, 5, and 6 in the next row, and so on; the first 26 such rows are shown below; the 26<sup>th<\/sup> starts with 326:<\/span><\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-50451 size-full\" src=\"https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021-1.jpg\" alt=\"\" width=\"766\" height=\"645\" srcset=\"https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021-1.jpg 766w, https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021-1-300x253.jpg 300w, https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021-1-640x539.jpg 640w\" sizes=\"auto, (max-width: 766px) 100vw, 766px\" \/><\/p>\n<ul>\n<li><span style=\"font-weight: 400\">The numbers on the left-hand side of the triangle (numbers in blue) are the so-called pancake numbers (also called lazy caterer\u2019s numbers and central polygonal numbers):<\/span><\/li>\n<\/ul>\n<p style=\"padding-left: 80px\"><span style=\"font-weight: 400\">\u25cb<\/span> <span style=\"font-weight: 400\">Slice a pancake once and you get two pieces; add a slice and you get four pieces; add a third slice and you get, not eight, but seven pieces; four slices give you 11 pieces, five give you 16 (see the pictures below) and so on; if you slice 25 times you get 326 pieces<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-50452\" src=\"https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021_2-1.jpg\" alt=\"\" width=\"758\" height=\"515\" srcset=\"https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021_2-1.jpg 758w, https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021_2-1-300x204.jpg 300w, https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021_2-1-640x435.jpg 640w\" sizes=\"auto, (max-width: 758px) 100vw, 758px\" \/><\/p>\n<ul>\n<li><span style=\"font-weight: 400\">The numbers on the right-hand side of Foyle\u2019s triangle (the numbers in green) are the triangular numbers<\/span><\/li>\n<li><span style=\"font-weight: 400\">The circled triangular numbers are doubly triangular: the first triangular numbers are 1, 3, 6, 10, 15, and 21; the 3<sup>rd<\/sup> triangular number (T<sub>3<\/sub>) is 6; T<sub>6<\/sub> is 21; T<sub>10<\/sub> is 55; T<sub>15<\/sub> is 120; T<sub>21<\/sub> is 231; and so on; these are the doubly triangular numbers<\/span><\/li>\n<li><span style=\"font-weight: 400\">The numbers in black on the far right of Foyle\u2019s triangle are the sums of the numbers in the corresponding rows; these numbers are the constants of the magic squares that contain the integers from 1 to n<sup>2<\/sup>, where n is the number of the row; for example, 15 is the sum in row 3 and it is the constant of a 3 \u00d7 3 magic square containing the integers 1 to 9; 34 (row 4) is the constant of a 4 \u00d7 4 magic square containing the integers 1 to 16; 65 (row 5) is the constant of a 5 \u00d7 5 magic square containing the integers 1 to 25; and so on:<\/span><\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-50453\" src=\"https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021_3.jpg\" alt=\"\" width=\"769\" height=\"365\" srcset=\"https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021_3.jpg 769w, https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021_3-300x142.jpg 300w, https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021_3-640x304.jpg 640w\" sizes=\"auto, (max-width: 769px) 100vw, 769px\" \/><\/p>\n<p style=\"text-align: center\"><b>Toothpicks<\/b><\/p>\n<ul>\n<li><span style=\"font-weight: 400\">We have seen different types of toothpick patterns before (<\/span><a href=\"https:\/\/blogs.bmj.com\/bmj\/2021\/04\/16\/jeffrey-aronson-when-i-use-a-word-new-and-not-so-new-medical-words\"><span style=\"font-weight: 400\">here<\/span><\/a><span style=\"font-weight: 400\">, <\/span><a href=\"https:\/\/blogs.bmj.com\/bmj\/2021\/04\/26\/jeffrey-aronson-when-i-use-a-word-a-difficult-infection\"><span style=\"font-weight: 400\">here<\/span><\/a><span style=\"font-weight: 400\">, and <\/span><a href=\"https:\/\/blogs.bmj.com\/bmj\/2021\/05\/14\/jeffrey-aronson-when-i-use-a-word-omics\"><span style=\"font-weight: 400\">here<\/span><\/a><span style=\"font-weight: 400\">); 326 features in the toothpick pattern called leftist toothpicks.<\/span><\/li>\n<li><span style=\"font-weight: 400\">Starting with a single toothpick, add toothpicks at free ends, but when the toothpick is horizontal use only the left end; the first four steps are shown in (a), (b), (c), and (d) below:<\/span><\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-50454\" src=\"https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021_4.jpg\" alt=\"\" width=\"751\" height=\"114\" srcset=\"https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021_4.jpg 751w, https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021_4-300x46.jpg 300w, https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021_4-640x97.jpg 640w\" sizes=\"auto, (max-width: 751px) 100vw, 751px\" \/><\/p>\n<ul>\n<li><span style=\"font-weight: 400\">After 25 iterations you get 94 toothpicks:<\/span><\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-50455\" src=\"https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021_5.jpg\" alt=\"\" width=\"747\" height=\"485\" srcset=\"https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021_5.jpg 747w, https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021_5-300x195.jpg 300w, https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021_5-640x416.jpg 640w\" sizes=\"auto, (max-width: 747px) 100vw, 747px\" \/><\/p>\n<p>&nbsp;<\/p>\n<ul>\n<li><span style=\"font-weight: 400\">55 iterations would give you 326 toothpicks<\/span><\/li>\n<\/ul>\n<p style=\"text-align: center\"><b>Palindromes<\/b><\/p>\n<ul>\n<li><span style=\"font-weight: 400\">326 + 623 = 949, a palindrome<\/span><\/li>\n<li><span style=\"font-weight: 400\">326 is palindromic in both base 12 (232) and base 13 (1c1); it is the smallest number with that property<\/span><\/li>\n<\/ul>\n<p style=\"text-align: center\"><b>Primes and semiprimes<\/b><\/p>\n<ul>\n<li><span style=\"font-weight: 400\">326 is a semiprime, being the product of two primes, 2 \u00d7 163; it is the 104<sup>th<\/sup> semiprime, S<sub>104<\/sub><\/span><\/li>\n<li><span style=\"font-weight: 400\">It is also an emirpimes, since its reverse, 623 is a semiprime = 7 \u00d7 89<\/span><\/li>\n<li><span style=\"font-weight: 400\">326 = the 57th prime (P<sub>57<\/sub>) + 57 = 269 + 57<\/span><\/li>\n<li><span style=\"font-weight: 400\">326 is the sum of all the digits in the first 38 primes, from 2 to 163<\/span><\/li>\n<li><span style=\"font-weight: 400\">The sum of the first 326 primes is 325019, which is a prime<\/span><\/li>\n<li><span style=\"font-weight: 400\">326 is the sum of the first 14 odd primes<\/span><\/li>\n<li><span style=\"font-weight: 400\">326<sup>2<\/sup> = 106276, which is the sum of two consecutive primes = 53129 + 53147<\/span><\/li>\n<li><span style=\"font-weight: 400\">3<sup>3<\/sup> + 2<sup>2<\/sup> + 6<sup>6<\/sup> = 46687, which is a prime<\/span><\/li>\n<li><span style=\"font-weight: 400\">326 = 2 \u00d7 163; 2<sup>2<\/sup> + 163<sup>2<\/sup> = 26573, which is a prime<\/span><\/li>\n<li><span style=\"font-weight: 400\">There are 326 fours in all the four-digit primes<\/span><\/li>\n<li><span style=\"font-weight: 400\">1\/3 + 1\/2 + 1\/6 = 1; thus, the harmonic mean of the three digits is 3, which is a prime<\/span><\/li>\n<\/ul>\n<p style=\"text-align: center\"><b>Named numbers<\/b><\/p>\n<ul>\n<li><span style=\"font-weight: 400\">326 is a happy number: add 3<sup>2<\/sup> + 2<sup>2<\/sup> + 6<sup>2<\/sup> = 49; now add 4<sup>2<\/sup> + 9<sup>2<\/sup> = 97; repeat; since you eventually reach one, 326 is a happy number; see <\/span><a href=\"https:\/\/blogs.bmj.com\/bmj\/2020\/02\/21\/jeffrey-aronson-when-i-use-a-word-anamnesis\/\"><span style=\"font-weight: 400\">Interesting integer 262<\/span><\/a><span style=\"font-weight: 400\"> and the diagram below, which shows all the happy numbers up to 338, with 326 highlighted:<\/span><\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-50456\" src=\"https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021_6.jpg\" alt=\"\" width=\"766\" height=\"462\" srcset=\"https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021_6.jpg 766w, https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021_6-300x181.jpg 300w, https:\/\/blogs.bmj.com\/bmj\/files\/2021\/06\/aronson_11_june_2021_6-640x386.jpg 640w\" sizes=\"auto, (max-width: 766px) 100vw, 766px\" \/><\/p>\n<ul>\n<li><span style=\"font-weight: 400\">326 is an untouchable number, an integer that cannot be expressed as the sum of all the proper divisors of any other number<\/span><\/li>\n<\/ul>\n<p style=\"text-align: center\"><b>Sums of 326<\/b><\/p>\n<ul>\n<li><span style=\"font-weight: 400\">326 is the sum of three squares in six different ways: 1<sup>2<\/sup> + 1<sup>2<\/sup> + 18<sup>2<\/sup>; 1<sup>2<\/sup> + 6<sup>2<\/sup> + 17<sup>2<\/sup>; 1<sup>2<\/sup> + 10<sup>2<\/sup> + 15<sup>2<\/sup> ; 3<sup>2<\/sup> + 11<sup>2<\/sup> + 14<sup>2<\/sup>; 6<sup>2<\/sup> + 11<sup>2<\/sup> + 13<sup>2<\/sup>; and 7<sup>2<\/sup> + 9<sup>2<\/sup> + 14<sup>2<\/sup><\/span><\/li>\n<li><span style=\"font-weight: 400\">It is the sum of eight distinct squares = 1<sup>2<\/sup> + 2<sup>2<\/sup> + 3<sup>2<\/sup> + 5<sup>2<\/sup> + 6<sup>2<\/sup> + 7<sup>2<\/sup> + 9<sup>2<\/sup> + 11<sup>2<\/sup><\/span><\/li>\n<li><span style=\"font-weight: 400\">It is the sum of two triangular numbers in two different ways:<\/span><\/li>\n<\/ul>\n<p style=\"padding-left: 40px\"><span style=\"font-weight: 400\">\u25cb<\/span> <span style=\"font-weight: 400\"> T<sub>1<\/sub> + T<sub>25<\/sub> = 1 + 325<\/span><\/p>\n<p style=\"padding-left: 40px\"><span style=\"font-weight: 400\">\u25cb<\/span> <span style=\"font-weight: 400\"> T<sub>16<\/sub> + T<sub>19<\/sub> = 136 + 190<\/span><\/p>\n<ul>\n<li><span style=\"font-weight: 400\">It is the sum of four consecutive numbers:<\/span><\/li>\n<\/ul>\n<p style=\"padding-left: 40px\"><span style=\"font-weight: 400\">\u25cb<\/span> <span style=\"font-weight: 400\"> 80 + 81 + 82 + 83<\/span><\/p>\n<ul>\n<li><span style=\"font-weight: 400\"> It is the sum of 14 consecutive primes:<\/span><\/li>\n<\/ul>\n<p style=\"padding-left: 40px\"><span style=\"font-weight: 400\">\u25cb 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47<\/span><\/p>\n<ul>\n<li><span style=\"font-weight: 400\"> It is the sum of five consecutive composite numbers in two different ways:<\/span><\/li>\n<\/ul>\n<p style=\"padding-left: 40px\"><span style=\"font-weight: 400\">\u25cb 63 + 64 + 65 + 66 + 68<\/span><\/p>\n<p style=\"text-align: center\"><b>Pythagoras<\/b><\/p>\n<ul>\n<li><span style=\"font-weight: 400\"> There is one Pythagorean triples that includes 326 as a leg:<\/span><\/li>\n<\/ul>\n<p style=\"padding-left: 80px\"><span style=\"font-weight: 400\">326, 26568, 26570; it is a multiple of 163, 13284, 13285<\/span><\/p>\n<p style=\"text-align: center\"><b>Fibonacci<\/b><\/p>\n<ul>\n<li><span style=\"font-weight: 400\">Start with 0, 0, 1; add the three numbers = 1; append it to the sequence and add the last three numbers = 2; continue; these numbers are called tribonacci numbers:<\/span><\/li>\n<\/ul>\n<p style=\"padding-left: 80px\"><span style=\"font-weight: 400\">0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, \u2026<\/span><\/p>\n<p style=\"padding-left: 80px\"><span style=\"font-weight: 400\">326 is the sum of the first 12 tribonacci numbers<\/span><\/p>\n<p>&nbsp;<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>Continuing my search for biomedical black swans, based on the words newly cited in the Oxford English Dictionary (OED) from 1970 to 2020, I now turn to terms relevant to [&#8230;]<\/p>\n<p><a class=\"btn btn-secondary understrap-read-more-link\" href=\"https:\/\/blogs.bmj.com\/bmj\/2021\/06\/11\/jeffrey-aronson-when-i-use-a-word-black-swans-in-microbiology\/\">More&#8230;<\/a><\/p>\n","protected":false},"author":419,"featured_media":38359,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5762],"tags":[],"class_list":["post-50441","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-jeff-aronsons-words"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Jeffrey Aronson: When I Use a Word . . . 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