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

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, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110

Offset: 0

Author

Henry Bottomley, Jun 06 2000

Keywords

• base
• easy
• nonn

Comments

From Wolfdieter Lang, Jan 16 2018: (Start)

The symbols used for 0..9 in this base 60 notation are 00, 01, ..., 09, but leading zeros are omitted.

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.

(End)

For n < 1440, US and NATO military time designation of n minutes since midnight. - J. Lowell, Dec 29 2020

References

• 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.
• 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.
• Georges Ifrah, Histoire Universelle des Chiffres, Paris, 1981.
• Georges Ifrah, From one to zero, A universal history of numbers, Viking Penguin Inc., 1985.
• Georges Ifrah, Universalgeschichte der Zahlen, Campus Verlag, Frankfurt, New York, 2. Auflage, 1987, pp. 210-221.

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..10000
• Wolfdieter Lang, Sumerian-Babylonian sexagesimal-decimal number system.

Crossrefs

Cf. A049872, A131650,

Note also that A250073 = a(A000079(n)), A250089 = a(A051037(n)), A254334 = a(A000244(n)), A254335 = a(A000351(n)), A254336 = a(A011557(n)).

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).

Programs

Mathematica

Array[FromDigits@ Apply[Join, PadLeft[#, 2] & /@ IntegerDigits@ IntegerDigits[#, 60]] &, 71, 0] (* Michael De Vlieger, Jan 11 2018 *)

PARI

A055643(n)=fromdigits(digits(n,60),100) \\ M. F. Hasler, Jan 09 2018

Python

def a(n): return n if n < 60 else 100*a(n//60) + n%60
print([a(n) for n in range(71)]) # Michael S. Branicky, Oct 22 2022

Formula

a(60*n+r) = 100*a(n) + r, 0 <= r <= 59. - Jianing Song, Oct 22 2022

Extensions

a(69) and a(70) from WG Zeist, Sep 08 2012