cp's OEIS Frontend

A200066 Marks found on the Ishango bone in nondecreasing order.

%I A200066 #61 Jul 25 2024 14:01:08
%S A200066 3,4,5,5,6,7,8,9,10,11,11,13,17,19,19,21
%N A200066 Marks found on the Ishango bone in nondecreasing order.
%C A200066 The Ishango bone appears to be the oldest known mathematical object that contains an integer sequence with distinct numbers, dated from 18000 to 20000 BC. The oldest known tally stick is the Lebombo bone which is a piece of baboon fibula with 29 notches, dated 35000 BC. Note that A100000 shows only the "middle column" of Ishango bone. This sequence lists all terms of the three columns of the bone in nondecreasing order.
%D A200066 M. Grousson, "Depuis quand compte-t-on ?" in 'Science & Vie', pp. 58-61, No. 1080 2007 Mondadori/Excelsior Publications Paris.
%D A200066 D. Huylebrouck, "L'Afrique, berceau des mathématiques", in Mathématiques exotiques pp. 46-50, Dossier No. 47, Pour La Science 2005 Paris.
%D A200066 D. Huylebrouck and V. Pletser, The Ishango artifact: the missing base 12 link, Proc. Katachi Univ. Symmetry Congress (KUS2), Paper C11, Tsukuba Univ., Japan, 18 Nov. 1999; Forma 14-4, 339-346.
%D A200066 G. G. Joseph, The Crest of the Peacock: Non-European Roots of Mathematics, Penguin Books, London, 1992.
%D A200066 Richard Mankiewicz, The Story of Mathematics, Weidenfeld Nicolson Illustrated; New Ed edition (September 13, 2001).
%D A200066 D. Olivastro, Ancient Puzzles, Chap. 1 "The First Etches" pp. 7-30 Bantam Books NY 1993.
%D A200066 Claudia Zaslavsky, Africa Counts, Lawrence Hill Books, New York, 1973.
%H A200066 AfricaMaat, <a href="http://africamaat.com/Africa-The-true-cradle-of">Africa: The true cradle of mathematical sciences</a> [broken/unusable link]
%H A200066 J. Bogoshi, K. Naidoo and J. Webb, <a href="http://www.jstor.org/stable/3617049">71.36 The oldest mathematical artifact</a>, Math. Gazette, 71:458 (1987) 294.
%H A200066 Brussels Museum for Natural Sciences, <a href="https://web.archive.org/web/20110502042418/http://www.naturalsciences.be/expo/old_ishango/en/">The Ishango Bone Exhibition</a>.
%H A200066 C. K. Caldwell, The Prime Glossary, <a href="http://www.utm.edu/research/primes/glossary/IshangoBone.html">Ishango bone</a>
%H A200066 Wikipedia, <a href="http://en.wikipedia.org/wiki/Ishango_bone">Ishango bone</a>
%H A200066 S. W. Williams, <a href="http://www.math.buffalo.edu/mad/Ancient-Africa/ishango.html">Mathematicians of the Africa diaspora. Ishango bone</a>
%e A200066 The three columns (or rows) of the Ishango bone are
%e A200066 [3, 6, 4, 8, 10, 5, 5, 7], [11, 13, 17, 19], [11, 21, 19, 9]. Or [11, 13, 17, 19], [11, 21, 19, 9], [3, 6, 4, 8, 10, 5, 5, 7]. Or [11, 21, 19, 9], [3, 6, 4, 8, 10, 5, 5, 7], [11, 13, 17, 19].
%e A200066 In reverse order, the three columns (or rows) are
%e A200066 [9, 19, 21, 11], [19, 17, 13, 11], [7, 5, 5, 10, 8, 4, 6, 3]. Or [19, 17, 13, 11], [7, 5, 5, 10, 8, 4, 6, 3], [9, 19, 21, 11]. Or [7, 5, 5, 10, 8, 4, 6, 3], [9, 19, 21, 11], [19, 17, 13, 11].
%Y A200066 Cf. A100000.
%K A200066 nonn,fini,full
%O A200066 1,1
%A A200066 _Omar E. Pol_, Nov 14 2011