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

0,3

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.

Formula

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

Mathematica

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

Prog

(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

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).

Sequence in context: A265711 A262065 A296765 * A122079 A272118 A247163

Adjacent sequences: A055640 A055641 A055642 * A055644 A055645 A055646

Keyword

base,easy,nonn

Author

Henry Bottomley, Jun 06 2000

Extensions

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

Status

approved