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 1-10 of 14 results. Next

A096347 Least number with n preimages (or immediate predecessors) under f(n) = n + (product of nonzero digits of n).

Original entry on oeis.org

1, 2, 12, 102, 116, 1098, 2072, 1014, 101134, 11014, 1011098, 1003525, 41021255, 210110985, 403130555, 481104655, 4401225555, 4811125555, 86413249555, 39011218055
Offset: 0

Views

Author

Jason Earls, Jun 29 2004

Keywords

Comments

First occurrence of k in A096972.
a(20) > 10^11. [From Donovan Johnson, Nov 22 2009]

Examples

			a(3)=102 because 102 is the least number with three direct predecessors, 66: 66+6*6 = 102, 74: 74+7*4 = 102, 101: 101+1*1 = 102.

References

  • P. A. Loomis, An Introduction to Digit Product Sequences (see link).

Links

Crossrefs

Cf. A096972, A063108, A063425, A096922, A096923, A096924, A096925, A096926, A096927, A096928, A096929, A096930, A096931.

Extensions

a(8) to a(11) from Klaus Brockhaus, Jul 07 2004
a(12) from Robert G. Wilson v, Jul 15 2004
a(13)-a(19) from Donovan Johnson, Nov 22 2009

A096931 Numbers n for which there are exactly ten k such that n = k + (product of nonzero digits of k).

Original entry on oeis.org

1011098, 2102125, 2411305, 2711105, 4012055, 4042055, 4086725, 4101455, 4105555, 4132755, 4310145, 6021254, 6621256, 8012765, 8013495, 8111255, 8202555, 9012405, 9302165, 10011116, 10111014, 10113255, 11011098, 12102125
Offset: 1

Views

Author

Klaus Brockhaus, Jul 15 2004

Keywords

Examples

			965738, 978842, 988058, 991658, 1009397, 1010874, 1010936, 1010972, 1011058 and 1011082 are the only ten k such that k + (product of nonzero digits of k) = 1011098, hence 1011098 is a term.

Crossrefs

Cf. A063114, A096347, A096922, A096923, A096924, A096925, A096926, A096927, A096928, A096929, A096930.

Programs

  • Mathematica
    f[n_] := Block[{s = Sort[ IntegerDigits[n]]}, While[ s[[1]] == 0, s = Drop[s, 1]]; n + Times @@ s]; t = Table[0, {12500000}]; Do[ a = f[n]; If[a < 12500000, t[[a]]++ ], {n, 12500000}]; Do[ If[ t[[n]] == 10, Print[n]], {n, 12500000}] (* Robert G. Wilson v, Jul 16 2004 *)
  • PARI
    {c=10;z=3000000;v=vector(z);for(n=1,z+1,k=addpnd(n);if(k<=z,v[k]=v[k]+1));for(j=1,length(v),if(v[j]==c,print1(j,",")))} \\for function addpnd see A096922

Extensions

More terms from Robert G. Wilson v, Jul 16 2004

A096926 Numbers n for which there are exactly five k such that n = k + (product of nonzero digits of k).

Original entry on oeis.org

1098, 1126, 1180, 1272, 1474, 1546, 1564, 2014, 2125, 2418, 3180, 3230, 3442, 5222, 5358, 5640, 6245, 7185, 7666, 8155, 8173, 8412, 9214, 9229, 9450, 9518, 10074, 10102, 10110, 10134, 10212, 10228, 10355, 10445, 10455, 10474, 10546, 10827
Offset: 1

Views

Author

Klaus Brockhaus, Jul 15 2004

Keywords

Examples

			937, 982, 1077, 1118 and 1122 are the only five k such that k + (product of nonzero digits of k) = 1126, hence 1126 is a term.

Crossrefs

Cf. A063114, A096347, A096922 - A096925, A096927 - A096931.

Programs

  • PARI
    {c=5;z=11000;v=vector(z);for(n=1,z+1,k=addpnd(n);if(k<=z,v[k]=v[k]+1));for(j=1,length(v),if(v[j]==c,print1(j,",")))} \\for function addpnd see A096922

A096924 Numbers n for which there are exactly three k such that n = k + (product of nonzero digits of k).

Original entry on oeis.org

102, 110, 118, 126, 134, 150, 180, 202, 216, 225, 234, 260, 272, 312, 338, 366, 404, 414, 420, 455, 456, 512, 534, 542, 564, 576, 586, 635, 645, 712, 734, 750, 786, 808, 818, 827, 837, 840, 894, 920, 939, 970, 980, 1018, 1020, 1034, 1042, 1072, 1074, 1075
Offset: 1

Views

Author

Klaus Brockhaus, Jul 15 2004

Keywords

Examples

			76, 109 and 114 are the only three k such that k + (product of nonzero digits of k) = 118, hence 118 is a term.

Crossrefs

Cf. A063114, A096347, A096922, A096923, A096925 - A096931.

Programs

  • PARI
    {c=3;z=1100;v=vector(z);for(n=1,z+1,k=addpnd(n);if(k<=z,v[k]=v[k]+1));for(j=1,length(v),if(v[j]==c,print1(j,",")))} \\for function addpnd see A096922

A096925 Numbers n for which there are exactly four k such that n = k + (product of nonzero digits of k).

Original entry on oeis.org

116, 405, 430, 474, 530, 546, 642, 744, 774, 836, 854, 855, 930, 958, 1038, 1055, 1070, 1088, 1104, 1110, 1116, 1134, 1154, 1162, 1236, 1366, 1400, 1405, 1418, 1430, 1455, 1530, 1642, 1744, 1774, 1836, 1854, 1855, 1930, 1958, 2112, 2137, 2185, 2199, 2205
Offset: 1

Views

Author

Klaus Brockhaus, Jul 15 2004

Keywords

Examples

			279, 345, 381 and 401 are the only four k such that k + (product of nonzero digits of k) = 405, hence 405 is a term.

Crossrefs

Cf. A063114, A096347, A096922 - A096924, A096926 - A096931.

Programs

  • Mathematica
    Take[Select[Tally[Table[k+Times@@(IntegerDigits[k]/.(0->1)),{k,100000}]],#[[2]] == 4&][[All,1]]//Sort,50] (* Harvey P. Dale, Oct 12 2022 *)
  • PARI
    {c=4;z=2210;v=vector(z);for(n=1,z+1,k=addpnd(n);if(k<=z,v[k]=v[k]+1));for(j=1,length(v),if(v[j]==c,print1(j,",")))} \\for function addpnd see A096922

A096927 Numbers n for which there are exactly six k such that n = k + (product of nonzero digits of k).

Original entry on oeis.org

2072, 3525, 9170, 9190, 11098, 11116, 11474, 11564, 12072, 12125, 13525, 19170, 19190, 20165, 20228, 20445, 21125, 24305, 29395, 30488, 31105, 31255, 31305, 31825, 40339, 40344, 40455, 41255, 42355, 45555, 50745, 51175, 54742, 58300
Offset: 1

Views

Author

Klaus Brockhaus, Jul 15 2004

Keywords

Examples

			1688, 1928, 1991, 2036, 2052 and 2060 are the only six k such that k + (product of nonzero digits of k) = 2072, hence 2072 is a term.

Crossrefs

Cf. A063114, A096347, A096922 - A096926, A096928 - A096931.

Programs

  • Mathematica
    With[{nn=60000},Select[Tally[Table[n+Times@@(IntegerDigits[n]/.(0->1)),{n,nn}]],#[[2]]==6&&#[[1]]<=nn&]][[All,1]]//Sort(* Harvey P. Dale, Aug 16 2018 *)
  • PARI
    {c=6;z=60000;v=vector(z);for(n=1,z+1,k=addpnd(n);if(k<=z,v[k]=v[k]+1));for(j=1,length(v),if(v[j]==c,print1(j,",")))} \\for function addpnd see A096922

A096928 Numbers n for which there are exactly seven k such that n = k + (product of nonzero digits of k).

Original entry on oeis.org

1014, 8305, 18305, 26425, 30205, 30725, 31414, 39186, 41156, 51358, 71110, 71136, 72505, 74470, 80305, 82765, 90985, 100405, 100786, 100855, 101014, 101098, 101126, 102072, 110474, 112418, 118305, 126425, 130205, 130725, 131414, 139186
Offset: 1

Views

Author

Klaus Brockhaus, Jul 15 2004

Keywords

Examples

			678, 854, 933, 942, 960, 1007 and 1012 are the only seven k such that k + (product of nonzero digits of k) = 1014, hence 1014 is a term.

Crossrefs

Cf. A063114, A096347, A096922 - A096927, A096929 - A096931.

Programs

  • Mathematica
    Select[Tally[Table[n+Times@@Select[IntegerDigits[n],#!=0&],{n,200000}]], #[[2]] == 7&][[All,1]]//Sort (* Harvey P. Dale, Apr 21 2018 *)
  • PARI
    {c=7;z=140000;v=vector(z);for(n=1,z+1,k=addpnd(n);if(k<=z,v[k]=v[k]+1));for(j=1,length(v),if(v[j]==c,print1(j,",")))} \\for function addpnd see A096922

A096929 Numbers n for which there are exactly eight k such that n = k + (product of nonzero digits of k).

Original entry on oeis.org

101134, 101180, 101642, 108305, 204205, 216425, 220145, 220725, 231014, 271855, 283055, 291705, 300180, 301205, 302125, 303555, 330776, 405555, 442055, 442395, 464255, 492055, 604425, 621136, 691865, 702145, 711486, 723205, 733585, 784985
Offset: 1

Views

Author

Klaus Brockhaus, Jul 15 2004

Keywords

Examples

			88846, 97354, 98254, 99514, 100954, 101078, 101086 and 101131 are the only eight k such that k + (product of nonzero digits of k) = 101134, hence 101134 is a term.

Crossrefs

Cf. A063114, A096347, A096922 - A096928, A096930, A096931.

Programs

  • PARI
    {c=8;z=800000;v=vector(z);for(n=1,z+1,k=addpnd(n);if(k<=z,v[k]=v[k]+1));for(j=1,length(v),if(v[j]==c,print1(j,",")))} \\for function addpnd see A096922

A063425 Unattainable numbers: integers not expressible as k + product of nonzero digits of k (A063114).

Original entry on oeis.org

1, 3, 5, 7, 9, 13, 15, 17, 19, 21, 25, 27, 30, 31, 36, 37, 39, 40, 43, 48, 49, 51, 52, 53, 57, 59, 61, 63, 64, 69, 71, 72, 73, 76, 79, 82, 83, 84, 87, 90, 91, 93, 96, 97, 103, 105, 113, 115, 117, 119, 121, 127, 131, 136, 137, 139, 148, 149, 151, 153, 157, 159, 163, 164
Offset: 1

Views

Author

Robert G. Wilson v, Aug 09 2001

Keywords

Links

Crossrefs

Cf. A063114, A096347, A063425, A096922, A096923, A096924, A096925, A096926, A096927, A096928, A096929, A096930, A096931.

Programs

  • Mathematica
    f[n_] := Block[{s = Sort[ IntegerDigits[n]]}, While[ s[[1]] == 0, s = Drop[s, 1]]; n + Times @@ s]; t = Table[0, {200}]; Do[ a = f[n]; If[a < 200, t[[a]]++ ], {n, 200}]; Select[ Range[ 200], t[[ # ]] == 0 &] (* Robert G. Wilson v, Jul 16 2004 *)

A096923 Numbers n for which there are exactly two k such that n = k + (product of nonzero digits of k).

Original entry on oeis.org

12, 14, 16, 18, 22, 26, 38, 44, 50, 55, 62, 66, 74, 80, 86, 88, 98, 104, 112, 114, 120, 122, 123, 138, 142, 144, 155, 160, 162, 166, 170, 174, 186, 188, 198, 209, 210, 212, 218, 224, 230, 237, 240, 250, 258, 261, 265, 285, 286, 294, 303, 308, 314, 316, 326, 327
Offset: 1

Views

Author

Klaus Brockhaus, Jul 15 2004

Keywords

Examples

			18 and 22 are the only two k such that k + (product of nonzero digits of k) = 26, hence 26 is a term.

Crossrefs

Cf. A063114, A096347, A096922, A096924 - A096931.

Programs

  • Mathematica
    knzd[n_]:=n+Times@@Select[IntegerDigits[n],#!=0&]; Sort[Transpose[ Select[ Tally[ Array[ knzd,400]],Last[#]==2&]][[1]]] (* Harvey P. Dale, Nov 05 2013 *)
  • PARI
    {c=2;z=330;v=vector(z);for(n=1,z+1,k=addpnd(n);if(k<=z,v[k]=v[k]+1));for(j=1,length(v),if(v[j]==c,print1(j,",")))} \\for function addpnd see A096922
Showing 1-10 of 14 results. Next

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