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A055643 Babylonian numbers: integers in base 60 with each sexagesimal digit represented by 2 decimal digits, leading zeros omitted.

%I A055643 #55 Oct 22 2022 20:47:04
%S A055643 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,
%T A055643 26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,
%U A055643 49,50,51,52,53,54,55,56,57,58,59,100,101,102,103,104,105,106,107,108,109,110
%N A055643 Babylonian numbers: integers in base 60 with each sexagesimal digit represented by 2 decimal digits, leading zeros omitted.
%C A055643 From _Wolfdieter Lang_, Jan 16 2018: (Start)
%C A055643 The symbols used for 0..9 in this base 60 notation are 00, 01, ..., 09, but leading zeros are omitted.
%C A055643 For the Sumerian-Babylonian sexagesimal-decimal number system which uses two positions for each base-60 position filled with only one-digit numbers alternating between ranges of 0 to 9 and 0 to 5 see the link below.
%C A055643 (End)
%C A055643 For n < 1440, US and NATO military time designation of n minutes since midnight. - _J. Lowell_, Dec 29 2020
%D A055643 Mohammad K. Azarian, Meftah al-hesab: A Summary, MJMS, Vol. 12, No. 2, Spring 2000, pp. 75-95. Mathematical Reviews, MR 1 764 526. Zentralblatt MATH, Zbl 1036.01002.
%D A055643 Mohammad K. Azarian, A Summary of Mathematical Works of Ghiyath ud-din Jamshid Kashani, Journal of Recreational Mathematics, Vol. 29(1), pp. 32-42, 1998.
%D A055643 Georges Ifrah, Histoire Universelle des Chiffres, Paris, 1981.
%D A055643 Georges Ifrah, From one to zero, A universal history of numbers, Viking Penguin Inc., 1985.
%D A055643 Georges Ifrah, Universalgeschichte der Zahlen, Campus Verlag, Frankfurt, New York, 2. Auflage, 1987, pp. 210-221.
%H A055643 Michael De Vlieger, <a href="/A055643/b055643.txt">Table of n, a(n) for n = 0..10000</a>
%H A055643 Wolfdieter Lang, <a href="/A055643/a055643.pdf">Sumerian-Babylonian sexagesimal-decimal number system.</a>
%F A055643 a(60*n+r) = 100*a(n) + r, 0 <= r <= 59. - _Jianing Song_, Oct 22 2022
%t A055643 Array[FromDigits@ Apply[Join, PadLeft[#, 2] & /@ IntegerDigits@ IntegerDigits[#, 60]] &, 71, 0] (* _Michael De Vlieger_, Jan 11 2018 *)
%o A055643 (PARI) A055643(n)=fromdigits(digits(n,60),100) \\ _M. F. Hasler_, Jan 09 2018
%o A055643 (Python)
%o A055643 def a(n): return n if n < 60 else 100*a(n//60) + n%60
%o A055643 print([a(n) for n in range(71)]) # _Michael S. Branicky_, Oct 22 2022
%Y A055643 Cf. A049872, A131650,
%Y A055643 Note also that A250073 = a(A000079(n)), A250089 = a(A051037(n)), A254334 = a(A000244(n)), A254335 = a(A000351(n)), A254336 = a(A011557(n)).
%Y A055643 See also A281863 (value of the 0,1,2,...,n-th digit of a(n), counted from the right), A282622 (length of a(n), #digits, for n >= 1).
%K A055643 base,easy,nonn
%O A055643 0,3
%A A055643 _Henry Bottomley_, Jun 06 2000
%E A055643 a(69) and a(70) from _WG Zeist_, Sep 08 2012