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: Marc Paulhus

Marc Paulhus's wiki page.

Marc Paulhus has authored 18 sequences. Here are the ten most recent ones:

A067972 a(n+1) is the smallest cube > a(n) such that the digits of a(n) are all (with multiplicity) properly contained in the digits of a(n+1), with a(0)=1.

Original entry on oeis.org

1, 125, 15625, 1157625, 311665752, 19356769125, 291566137591, 5131167956992, 110979523759616, 1295599371716096, 16597961902739125, 191569168079975232, 1081935177662959192, 10103177625989916259, 110151807092929695367
Offset: 0

Views

Author

Marc Paulhus, Feb 05 2002

Keywords

Crossrefs

Cf. A067971.

Formula

A067971^3

A067973 a(n+1) is the smallest number > a(n) such that the digits of a(n)^3 are all (with multiplicity) contained in the digits of a(n+1)^3, with a(0)=1.

Original entry on oeis.org

1, 5, 8, 25, 105, 678, 2685, 6631, 17248, 48056, 109016, 255085, 576468, 993996, 1026598, 1029697, 1061509, 1089598, 1231339, 1374358, 1753291, 1832389, 1896319, 2161819, 2162446, 2163199, 2231416, 2263201, 2264893, 2674003
Offset: 0

Views

Author

Marc Paulhus, Feb 05 2002

Keywords

Comments

If "contained in" is replaced by "properly contained in" we get A067971.

Examples

			5^3 = 125 and 8 is the next smallest number whose cube (in this case 512) that contains the digits 1,2,5.

Crossrefs

Cf. A067971, A065298, A067974, A014563, A065297.

A067975 a(n+1) is the smallest number > a(n) such that the digits of a(n)^2 are all (with multiplicity) contained in the digits of a(n+1)^2, with a(0)=2.

Original entry on oeis.org

2, 7, 43, 136, 367, 1157, 1822, 3658, 5558, 6196, 9679, 10183, 11794, 17852, 20813, 28354, 32193, 42852, 53787, 55044, 55707, 55983, 57636, 58464, 61719, 70209, 95232, 96354, 96921, 96963, 101407, 114223, 114323, 133564, 162293, 170843
Offset: 0

Views

Author

Marc Paulhus, Feb 05 2002

Keywords

Comments

a(n) for n>0 remains the same when a(0)=3. If "contained in" is replaced by "properly contained in" we get A065298.

Examples

			1157^2 = 1338649 and 1822 is the next smallest number whose square (in this case 3319684) contains the digits 1,3,3,8,6,4,9.

Crossrefs

Cf. A065297, A014563, A067971, A065298, A067973.

A067711 a(n+1) is the smallest square > a(n) such that the digits of a(n) are all (with multiplicity) properly contained in the digits of a(n+1), with a(0)=1.

Original entry on oeis.org

1, 16, 169, 1296, 12769, 237169, 1073296, 10329796, 109327936, 1353209796, 10193527369, 102179958336, 1003931857296, 10023359708961, 100035723189796, 1000257893937316, 10002783993738561, 100018367973835249
Offset: 0

Views

Author

Marc Paulhus, Feb 05 2002

Keywords

Crossrefs

Cf. A065297.

Formula

a(n) = A065297(n)^2.

A067714 a(n+1) is the smallest square > a(n) such that the digits of a(n) are all (with multiplicity) properly contained in the digits of a(n+1), with a(0)=4.

Original entry on oeis.org

4, 49, 1849, 18496, 134689, 1338649, 13380964, 103693489, 1036389249, 10283379649, 102743968369, 1003687392964, 10026487930369, 100038463697929, 1000274339968996, 10003462899739969, 100234979989639056
Offset: 0

Views

Author

Marc Paulhus, Feb 05 2002

Keywords

Comments

a(n) for n>0 remains the same when a(0)=9

Crossrefs

Cf. A065298.

Formula

a(n) = A065298(n)^2.

A067713 a(n+1) is the smallest square > a(n) such that the digits of a(n) are all (with multiplicity) contained in the digits of a(n+1), with a(0)=1.

Original entry on oeis.org

1, 16, 169, 196, 961, 1296, 2916, 9216, 12769, 96721, 237169, 729316, 1073296, 1630729, 2709316, 10329796, 69739201, 109327936, 130279396, 133079296, 133702969, 309971236, 317302969, 917302369, 1353209796, 1725903936
Offset: 0

Views

Author

Marc Paulhus, Feb 05 2002

Keywords

Crossrefs

Cf. A014563.

Formula

a(n) = A014563(n)^2.

A067717 a(n+1) is the smallest square > a(n) such that the digits of a(n) are all (with multiplicity) contained in the digits of a(n+1), with a(0)=4.

Original entry on oeis.org

4, 49, 1849, 18496, 134689, 1338649, 3319684, 13380964, 30891364, 38390416, 93683041, 103693489, 139098436, 318693904, 433180969, 803949316, 1036389249, 1836293904, 2893041369, 3029841936, 3103269849, 3134096289, 3321908496
Offset: 0

Views

Author

Marc Paulhus, Feb 05 2002

Keywords

Comments

a(n) for n>0 remains the same when a(0)=9.

Crossrefs

Cf. A067975.

Formula

a(n) = A067975(n)^2.

A067971 a(n+1) is the smallest number > a(n) such that the digits of a(n)^3 are all (with multiplicity) properly contained in the digits of a(n+1)^3, with a(0)=1.

Original entry on oeis.org

1, 5, 25, 105, 678, 2685, 6631, 17248, 48056, 109016, 255085, 576468, 1026598, 2161819, 4793623, 10107506, 21624889, 46584891, 100042239, 215671305, 464309988, 1000305876, 2156229901, 4642492109, 10000266599
Offset: 0

Views

Author

Marc Paulhus, Feb 05 2002

Keywords

Examples

			5^3 = 125 and 25 is the next smallest number whose cube (in this case 15625) properly contains the digits 1,2,5.

Crossrefs

Cf. A000578, A065297, A065298, A067972.

Extensions

a(22)-a(24) from Sean A. Irvine, Jan 16 2024

A067974 a(n+1) is the smallest cube > a(n) such that the digits of a(n) are all (with multiplicity) contained in the digits of a(n+1), with a(0)=1.

Original entry on oeis.org

1, 125, 512, 15625, 1157625, 311665752, 19356769125, 291566137591, 5131167956992, 110979523759616, 1295599371716096, 16597961902739125, 191569168079975232, 982095927615711936, 1081935177662959192, 1091762925561991873, 1196109781753695229, 1293596679780115192
Offset: 0

Views

Author

Marc Paulhus, Feb 05 2002

Keywords

Crossrefs

Cf. A000578, A067973.

Formula

a(n) = A067973(n)^3.

Extensions

More terms from Sean A. Irvine, Jan 16 2024

A014563 a(n+1) is the smallest number > a(n) such that the digits of a(n)^2 are all (with multiplicity) contained in the digits of a(n+1)^2, with a(0)=1.

Original entry on oeis.org

1, 4, 13, 14, 31, 36, 54, 96, 113, 311, 487, 854, 1036, 1277, 1646, 3214, 8351, 10456, 11414, 11536, 11563, 17606, 17813, 30287, 36786, 41544, 54927, 56547, 56586, 57363, 62469, 62634, 72813, 72897, 76944, 78345, 95061, 97944, 100963, 101944
Offset: 0

Views

Author

Marc Paulhus, Jan 29 2002

Keywords

Comments

Probably infinite. - David W. Wilson, Jan 29 2002

Examples

			13^2 = 169 and 14 is the next smallest number whose square (in this case 196) contains the digits 1,6,9.

Links

Crossrefs

If "contained in" is replaced by "properly contained in" we get A065297.
Cf. A066825, A067633, A067634, A067635, A065297.
Cf. A000290, A000196.

Programs

  • Haskell
    import Data.List ((\\))
a014563 n = a014563_list !! n
a014563_list = 1 : f 1 (drop 2 a000290_list) where
   f x (q:qs) | null $ xs \\ (show q) = y : f y qs
              | otherwise             = f x qs
              where y = a000196 q; xs = show (x * x)
-- Reinhard Zumkeller, Nov 22 2012
  • Mathematica
    snd[n_]:=Module[{k=n+1},While[!AllTrue[Select[Transpose[{DigitCount[n^2],
DigitCount[k^2]}],#[[1]]>0&],#[[1]]<=#[[2]]&],k++];k]; NestList[ snd,1,40] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 21 2016 *)

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