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 1-6 of 6 results.

A111117 Divisors of 10^15 - 1.

Original entry on oeis.org

1, 3, 9, 27, 31, 37, 41, 93, 111, 123, 271, 279, 333, 369, 813, 837, 999, 1107, 1147, 1271, 1517, 2439, 3441, 3813, 4551, 7317, 8401, 10027, 10323, 11111, 11439, 13653, 25203, 30081, 30969, 33333, 34317, 40959, 47027, 75609, 90243, 99999, 141081
Offset: 1

Views

Author

Douglas Winston (douglas.winston(AT)srupc.com), Oct 15 2005

Keywords

Links

Crossrefs

Cf. A018282, A018766, A027894, A027893, A027892, A027891, A027890, A027889, A027895, A027896, A027897, A109933, A106305, A001270, A007138, A046107, A112505.

Programs

A111211 Divisors of 10^16 - 1.

Original entry on oeis.org

1, 3, 9, 11, 17, 33, 51, 73, 99, 101, 137, 153, 187, 219, 303, 411, 561, 657, 803, 909, 1111, 1233, 1241, 1507, 1683, 1717, 2329, 2409, 3333, 3723, 4521, 5151, 6987, 7227, 7373, 9999, 10001, 11169, 13563, 13651, 13837, 15453, 18887, 20961, 22119, 25619
Offset: 1

Views

Author

Douglas Winston (douglas.winston(AT)srupc.com), Oct 25 2005

Keywords

Links

Crossrefs

Cf. A018282, A018766, A027894, A027893, A027892, A027891, A027890, A027889, A027895, A027896, A027897, A109933, A106305, A111117, A001270, A007138, A046107, A112505.

Programs

A113522 Divisors of 10^18 - 1.

Original entry on oeis.org

1, 3, 7, 9, 11, 13, 19, 21, 27, 33, 37, 39, 57, 63, 77, 81, 91, 99, 111, 117, 133, 143, 171, 189, 209, 231, 247, 259, 273, 297, 333, 351, 399, 407, 429, 481, 513, 567, 627, 693, 703, 741, 777, 819, 891, 999, 1001, 1053, 1197, 1221, 1287, 1443, 1463, 1539, 1729
Offset: 1

Views

Author

Douglas Winston (douglas.winston(AT)srupc.com), Jan 12 2006

Keywords

Links

Crossrefs

Cf. A018282, A018766, A027894, A027893, A027892, A027891, A027890, A027889, A027895, A027896, A027897, A109933, A106305, A111117, A111211, A113116, A001270, A007138, A046107, A112505.

Programs

A113116 Divisors of 10^17 - 1.

Original entry on oeis.org

1, 3, 9, 2071723, 6215169, 18645507, 5363222357, 16089667071, 48269001213, 11111111111111111, 33333333333333333, 99999999999999999
Offset: 1

Views

Author

Douglas Winston (douglas.winston(AT)srupc.com), Jan 02 2006

Keywords

Links

Crossrefs

Cf. A018282, A018766, A027894, A027893, A027892, A027891, A027890, A027889, A027895, A027896, A027897, A109933, A106305, A111117, A111211, A001270, A007138, A046107, A112505.

Programs

A226477 Table (read by rows) of the natural numbers (in ascending order) whose reciprocals have only periodic decimals of length k.

Original entry on oeis.org

1, 3, 9, 11, 33, 99, 27, 37, 111, 333, 999, 101, 303, 909, 1111, 3333, 9999, 41, 123, 271, 369, 813, 2439, 11111, 33333, 99999, 7, 13, 21, 39, 63, 77, 91, 117, 143, 189, 231, 259, 273, 297, 351, 407, 429, 481, 693, 777, 819, 1001, 1221, 1287, 1443, 2079, 2331, 2457, 2849, 3003, 3367, 3663, 3861, 4329, 5291, 6993, 8547, 9009, 10101, 10989, 12987, 15873, 25641, 27027, 30303, 37037, 47619, 76923, 90909, 111111, 142857, 333333, 999999
Offset: 1

Views

Author

Martin Renner, Jun 08 2013

Keywords

Comments

The k-th row always ends with 10^k - 1 = 99..99 (k times 9).
The number of elements in row k is A059892(k).

Examples

			The table T(k,m), m = 1..A059892(k), begins
  1, 3, 9;
  11, 33, 99;
  27, 37, 111, 333, 999;
  etc.

Links

Crossrefs

Cf. A018282, A018766, A027894, A027893, A027892, A027891, A027890, A027889, A027895, A027896, A027897, A109933, A106305, A111117, A111211, A113116, A113522 (Divisors of 10^k - 1, k = 2..18), A059892, A084680.

Programs

  • Maple
    a:=[1,3,9]: S:={1,3,9}: for k from 2 to 6 do T:=numtheory[divisors](10^k-1): a:=[op(a),op(T minus S)]: S:=S union T; od: a;
  • PARI
    Row(n) = my(v=divisors(10^n-1)); select(x->(znorder(Mod(10,x))==n), v) \\ Jianing Song, Jun 15 2021

A135365 a(n) = 3*a(n-1) - a(n-3) + 3*a(n-4), with initial values 1,3,9,11.

Original entry on oeis.org

1, 3, 9, 11, 33, 99, 313, 939, 2817, 8435, 25305, 75915, 227761, 683283, 2049849, 6149531, 18448593, 55345779, 166037353, 498112059, 1494336177, 4483008515, 13449025545, 40347076635, 121041229921, 363123689763, 1089371069289, 3268113207851, 9804339623553
Offset: 0

Views

Author

Paul Curtz, Dec 09 2007

Keywords

Links

Crossrefs

Cf. A018282, A027894, A106305.

Programs

  • Mathematica
    Join[{1, 3}, LinearRecurrence[{3, 0, -1, 3}, {9, 11, 33, 99}, 25]] (* G. C. Greubel, Oct 11 2016 *)
  • PARI
    Vec((1-15*x^3)/((1+x)*(1-3*x)*(1-x+x^2)) + O(x^40)) \\ Colin Barker, Feb 10 2016

Formula

From Richard Choulet, Jan 02 2008: (Start)
a(n) = (1/7)*3^(n+1) + (4/3)*(-1)^n - (16/21)*cos(Pi*n/3) + (16*sqrt(3)/7)*sin(Pi*n/3).
a(n) = (1/7)*3^(n+1) + (1/7)*[4; 12; 36; -4; -12; -36] for n>=0. (End)
G.f.: (1 - 15*x^3) / ((1+x)*(1-3*x)*(1-x+x^2)). - Colin Barker, Feb 10 2016
Showing 1-6 of 6 results.

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