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.

User: Stephen Tucker

Stephen Tucker's wiki page.

Stephen Tucker has authored 13 sequences. Here are the ten most recent ones:

A306036 a(n) is the period of the decimal expansion of 1/(100^n - 10^n - 1).

Original entry on oeis.org

44, 468, 496620, 16090340, 2499916380, 499999499999, 47368416315780, 71942445323740, 71428571357142857, 2413792682560590100, 661025543433488700, 998035336547180189380, 9826562531691739684620, 3086415088517393302531635, 33093525179856082014388489204
Offset: 1

Views

Author

Stephen Tucker, Jun 17 2018

Keywords

Comments

It appears that when Fibonacci numbers are written in base 10 diagonally (from top left to bottom right) such that each lower number is n digits farther to the right than its neighbor above, and the columns of digits are summed, the resulting total digit string recurs after a(n) digits.

Examples

			For n = 1: the Fibonacci numbers 1, 1, 2, 3, 5, 8, 13, when written in a diagonal, with each number 1 digit farther to the right than its predecessor, and the columns summed, gives the digit string 112359... . After this is extended to 44 numbers, the digit string has another occurrence of 112359. I conjecture that this is because the reciprocal of 89 has a period of 44 digits. It also demonstrates an amazing property of Fibonacci numbers.

Crossrefs

Cf. A007732, A021093 (1/89), A086695.

Programs

  • Mathematica
    Array[MultiplicativeOrder[10, (100^# - 10^# - 1)] &, 15] (* Michael De Vlieger, Jun 29 2018 *)
  • PARI
    a(n) = znorder(Mod(10, 100^n-10^n-1)) \\ Felix Fröhlich, Jun 18 2018

Extensions

More terms from Jon E. Schoenfield and Felix Fröhlich, Jun 18 2018

A260055 Composites whose prime factorization in base 12 is an anagram of the number in base 12.

Original entry on oeis.org

169, 185, 219, 2165, 2402, 3981, 4205, 10031, 21349, 21907, 22049, 24199, 26919, 27746, 28802, 29767, 29919, 31107, 46749, 71375, 251521, 252257, 252361, 259565, 275237, 280587, 292159, 293011, 301163, 303161, 305765
Offset: 1

Views

Author

Stephen Tucker, Jul 14 2015

Keywords

Examples

			169 = 13^2. In base 12, 121 = 11^2.

Links

Crossrefs

Cf. A260046, A260047, A260048, A260049, A260050, A260051, A260052, A260053, A025283, A260054.

Programs

  • PARI
    isok(n, b) = {f = factor(n); v = []; for (i=1, #f~, v = concat(v, digits(f[i,1], b)); if (f[i,2]!= 1, v = concat(v, digits(f[i,2], b)));); vecsort(v) == vecsort(digits(n, b));}
lista(nn, b=12) = forcomposite(n=1, nn, if (isok(n,b), print1(n, ", "))); \\ Michel Marcus, Jul 14 2015

A260054 Composites whose prime factorization in base 11 is an anagram of the number in base 11.

Original entry on oeis.org

4617, 7047, 18193, 33534, 180803, 196352, 217147, 283983, 386391, 422144, 448147, 616977, 705875, 842967, 886250, 926336, 947125, 954747, 1169536, 1235875, 1373375, 1866955, 1883049, 1968259
Offset: 1

Views

Author

Stephen Tucker, Jul 14 2015

Keywords

Examples

			4617 = 3^5 * 19. In base 11, 3518 = 3^5 * 18.

Links

Crossrefs

Cf. A260046, A260047, A260048, A260049, A260050, A260051, A260052, A260053, A025283, A260055.

Programs

  • Mathematica
    Select[Range[10^6], !PrimeQ[#] && Sort@ IntegerDigits[#, 11] == Sort@ Flatten@ IntegerDigits[ Select[ Flatten@ FactorInteger@ #, #>1 &], 11] &] (* Giovanni Resta, Jul 14 2015 *)

A260053 Composites whose prime factorization in base 9 is an anagram of the number in base 9.

Original entry on oeis.org

72646, 74176, 75295, 78475, 134832, 189771, 255619, 422233, 440561, 586022, 638582, 644799, 655312, 659712, 701078, 855296, 882278, 919488, 1197500, 1213750, 1328102, 1329280, 1428352, 1451968, 1581088, 1585184, 1718857
Offset: 1

Views

Author

Stephen Tucker, Jul 14 2015

Keywords

Examples

			72646 = 2 * 7 * 5189. In base 9, 120577 = 2 * 7 * 7105.

Links

Crossrefs

Cf. A260046, A260047, A260048, A260049, A260050, A260051, A260052, A025283, A260054, A260055.

Programs

  • Mathematica
    Select[Range[10^6], !PrimeQ[#] && Sort@ IntegerDigits[#, 9] == Sort@ Flatten@ IntegerDigits[ Select[ Flatten@ FactorInteger@ #, #>1 &], 9] &] (* Giovanni Resta, Jul 14 2015 *)

A260052 Composites whose prime factorization in base 8 is an anagram of the number in base 8.

Original entry on oeis.org

27, 85, 169, 175, 771, 4369, 4803, 5359, 6805, 7339, 19405, 21689, 24433, 36526, 40405, 40799, 41723, 41773, 43999, 44353, 46131, 47447, 48819, 49917, 54965, 71047, 74273, 87823, 107892, 130683, 131026, 139157, 246977, 268885, 269977
Offset: 1

Views

Author

Stephen Tucker, Jul 14 2015

Keywords

Examples

			27 = 3^3. In base 8, 33 = 3^3.

Links

Crossrefs

Cf. A260046, A260047, A260048, A260049, A260050, A260051, A260053, A025283, A260054, A260055.

Programs

  • Mathematica
    Select[Range[10^6], !PrimeQ[#] && Sort@ IntegerDigits[#, 8] == Sort@ Flatten@ IntegerDigits[ Select[ Flatten@ FactorInteger@ #, #>1 &], 8] &] (* Giovanni Resta, Jul 14 2015 *)

A260051 Composites whose prime factorization in base 7 is an anagram of the number in base 7.

Original entry on oeis.org

7136, 9056, 30057, 32076, 40256, 40678, 46400, 71125, 90334, 145152, 150027, 159975, 166281, 177315, 193227, 201057, 207681, 207843, 212000, 218080, 224192, 225195, 229407, 246777, 263031, 265184, 297027, 298144, 298208, 306624, 318096
Offset: 1

Views

Author

Stephen Tucker, Jul 14 2015

Keywords

Examples

			7136 = 2^5 * 223. In base 7, 26543 = 2^5 * 436.

Links

Crossrefs

Cf. A260046, A260047, A260048, A260049, A260050, A260052, A260053, A025283, A260054, A260055.

Programs

  • Mathematica
    Select[Range[10^5], !PrimeQ[#] && Sort@ IntegerDigits[#, 7] == Sort@ Flatten@ IntegerDigits[ Select[ Flatten@ FactorInteger@ #, #>1 &], 7] &] (* Giovanni Resta, Jul 14 2015 *)

A260050 Composites whose prime factorization in base 6 is an anagram of the number in base 6.

Original entry on oeis.org

16, 32, 49, 57, 314, 327, 377, 417, 575, 837, 1387, 1417, 1647, 1754, 1874, 1934, 1977, 2157, 2355, 2474, 2487, 2517, 2577, 2987, 3757, 5157, 5597, 7424, 8227, 9050, 9824, 10394, 10474, 10784, 10834, 11014, 11229, 11654, 11667, 12317, 12741, 13067
Offset: 1

Views

Author

Stephen Tucker, Jul 14 2015

Keywords

Examples

			16 = 2^4. In base 6, 24 = 2^4.

Links

Crossrefs

Cf. A260046, A260047, A260048, A260049, A260051, A260052, A260053, A025283, A260054, A260055.

A260049 Composites whose prime factorization in base 5 is an anagram of the number in base 5.

Original entry on oeis.org

2312, 2432, 3232, 5319, 5373, 10112, 10719, 11691, 14592, 15417, 19712, 20412, 21688, 22194, 23841, 24705, 25920, 26217, 32724, 36096, 39168, 41823, 42194, 42417, 43713, 51597, 58029, 59211, 61557, 62192, 66944, 67068, 68553, 72873, 76464
Offset: 1

Views

Author

Stephen Tucker, Jul 14 2015

Keywords

Examples

			2312 = 2^3 * 17^2. In base 5, 33222 = 2^3 * 32^2.

Links

Crossrefs

Cf. A260046, A260047, A260048, A260050, A260051, A260052, A260053, A025283, A260054, A260055.

Programs

  • Mathematica
    Select[Range[10^5], !PrimeQ[#] && Sort@ IntegerDigits[#, 5] == Sort@ Flatten@ IntegerDigits[ Select[ Flatten@ FactorInteger@ #, #>1 &], 5] &] (* Giovanni Resta, Jul 14 2015 *)

A260048 Composites whose prime factorization in base 4 is an anagram of the number in base 4.

Original entry on oeis.org

25, 637, 722, 1135, 1243, 1519, 1639, 1734, 1863, 2167, 4735, 4855, 4939, 5311, 5746, 5886, 5967, 6381, 6589, 6713, 7003, 7339, 7407, 7774, 8154, 8503, 8667, 8703, 9457, 11123, 11221, 11711, 15471, 16735, 17779, 17965, 18079, 18283, 18477, 18589
Offset: 1

Views

Author

Stephen Tucker, Jul 14 2015

Keywords

Examples

			25 = 5^2. In base 4, 121 = 11^2.

Links

Crossrefs

Cf. A260046, A260047, A260049, A260050, A260051, A260052, A260053, A025283, A260054, A260055.

Programs

  • Mathematica
    Select[Range[10^6], !PrimeQ[#] && Sort@ IntegerDigits[#, 4] == Sort@ Flatten@ IntegerDigits[ Select[ Flatten@ FactorInteger@ #, #>1 &], 4] &] (* Giovanni Resta, Jul 14 2015 *)

A260047 Composites whose prime factorization in base 3 is an anagram of the number in base 3.

Original entry on oeis.org

16, 25, 160, 960, 1125, 1888, 3146, 3488, 3549, 4064, 4235, 4335, 4928, 5415, 5746, 5875, 7502, 7847, 8224, 8414, 8954, 9633, 10016, 10192, 11840, 12103, 12256, 12704, 12716, 12844, 16415, 16820, 16954, 18784, 18880, 19264, 19355, 19481, 22838
Offset: 1

Views

Author

Stephen Tucker, Jul 14 2015

Keywords

Examples

			16 = 2^4. In base 3, 121 = 2^11.

Links

Crossrefs

Cf. A260046, A260048, A260049, A260050, A260051, A260052, A260053, A025283, A260054, A260055.

Programs

  • Mathematica
    Select[Range[10^6], !PrimeQ[#] && Sort@ IntegerDigits[#, 3] == Sort@ Flatten@ IntegerDigits[ Select[ Flatten@ FactorInteger@ #, #>1 &], 3] &] (* Giovanni Resta, Jul 14 2015 *)

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