cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-7 of 7 results.

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

Original entry on oeis.org

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

Views

Author

Henry Bottomley, Jun 06 2000

Keywords

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

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

A055645 Integers in base 16 with each hexadecimal digit represented by 2 decimal digits.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309
Offset: 0

Views

Author

Henry Bottomley, Jun 06 2000

Keywords

Links

Crossrefs

Cf. A049872.

Programs

  • Maple
    a:= proc(n) local i, m, r ; m:=n; r:=0;
      for i from 0 while m>0 do
        r:= r +100^i*irem(m, 16, 'm')
      od; r
   end:
seq(a(n), n=0..60);  # Alois P. Heinz, Jun 23 2014

A055649 Integers in base 11 with each base-11 digit represented by 2 decimal digits.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 500
Offset: 0

Views

Author

Henry Bottomley, Jun 06 2000

Keywords

Links

Crossrefs

Cf. A049872.

Programs

  • Maple
    a:= proc(n) local i, m, r ; m:=n; r:=0;
      for i from 0 while m>0 do
        r:= r +100^i*irem(m, 11, 'm')
      od; r
   end:
seq(a(n), n=0..82);  # Alois P. Heinz, Oct 07 2022

Extensions

Incorrect o.g.f. and linear recurrence removed by Georg Fischer, Oct 07 2022

A055644 Integers in base 20 with each base 20 digit represented by 2 decimal digits.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218
Offset: 0

Views

Author

Henry Bottomley, Jun 06 2000

Keywords

Crossrefs

Cf. A049872. First differs from A008554 when n=400, a(n)=10000 and A008554(n)=2000.

A055646 Integers in base 15 with each base 15 digit represented by 2 decimal digits.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311
Offset: 0

Views

Author

Henry Bottomley, Jun 06 2000

Keywords

Crossrefs

Cf. A049872.

A055647 Integers in base 14 with each base 14 digit represented by 2 decimal digits.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 400
Offset: 0

Views

Author

Henry Bottomley, Jun 06 2000

Keywords

Crossrefs

Cf. A049872.

A055648 Integers in base 13 with each base 13 digit represented by 2 decimal digits.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 400, 401, 402, 403, 404
Offset: 0

Views

Author

Henry Bottomley, Jun 06 2000

Keywords

Crossrefs

Cf. A049872.
Showing 1-7 of 7 results.

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