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.

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A029536 Numbers n such that n divides the (left) concatenation of all numbers <= n written in base 19 (most significant digit on right and removing all least significant zeros before concatenation).

Original entry on oeis.org

1, 3, 9, 21, 28, 36, 48, 87, 100, 156, 189, 208, 300, 547, 999, 1155, 1395, 1524, 3267, 6867, 7663, 8880, 9295, 30021, 38740, 49861, 86427, 379248, 454269, 657860, 850824, 1589897, 3523500, 8855295
Offset: 1

Views

Author

Olivier Gérard

Keywords

Comments

This sequence differs from A061972 in that all least significant zeros are removed before concatenation.
No more terms < 10^7. - Lars Blomberg, Sep 23 2011

Examples

			See A029519 for example.

Links

Crossrefs

Cf. A029447-A029470, A029471-A029494, A029495-A029518, A029519-A029542, A061931-A061954, A061955-A061978.

Programs

  • Mathematica
    b = 19; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[IntegerDigits[IntegerReverse[#, b], b], c], b], #] &] (* Robert Price, Mar 13 2020 *)
  • PARI
    lista(nn, m=19) = my(c, s, t); for(k=1, nn, t+=m^c*s=fromdigits(Vecrev(digits(k, m)), m); c+=logint(s, m)+1; if(t%k==0, print1(k, ", "))); \\ Jinyuan Wang, Dec 05 2020

Extensions

Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002
Additional comments and more terms from Larry Reeves (larryr(AT)acm.org), May 25 2001
a(29)-a(34) from Lars Blomberg, Sep 23 2011

A061939 Numbers n such that n divides the (right) concatenation of all numbers <= n written in base 10 (most significant digit on right).

Original entry on oeis.org

1, 2, 3, 5, 6, 9, 99, 153, 189, 238, 252, 323, 444, 539, 927, 3099, 3753, 4224, 5451, 8967, 44544, 53673, 97119, 1423719, 3860793, 4773591
Offset: 1

Views

Author

Larry Reeves (larryr(AT)acm.org), May 24 2001

Keywords

Comments

This sequence differs from A029503 in that all least significant zeros are removed before concatenation.
No more terms < 10^7. - Lars Blomberg, Oct 20 2011

Examples

			See A061931 for example.

Links

Crossrefs

Cf. A029447-A029470, A029471-A029494, A029495-A029518, A029519-A029542, A061931-A061954, A061955-A061978.

Programs

  • Mathematica
    b = 10; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[c, IntegerDigits[IntegerReverse[#, b], b]], b], #] &] (* Robert Price, Mar 08 2020 *)
  • PARI
    lista(nn, m=10) = my(s, t); for(k=1, nn, s=k/m^valuation(k, m); while(s, t=t*m+s%m; s\=m); if(t%k==0, print1(k, ", "))); \\ Jinyuan Wang, Dec 05 2020

Extensions

Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002
a(24)-a(26) from Lars Blomberg, Oct 20 2011

A061949 Numbers n such that n divides the (right) concatenation of all numbers <= n written in base 20 (most significant digit on right).

Original entry on oeis.org

1, 2, 4, 5, 6, 10, 12, 14, 18, 19, 57, 119, 133, 209, 399, 437, 633, 1102, 3517, 5719, 29849, 38532, 42759, 198639, 247801, 421591, 566561, 819185, 6781309
Offset: 1

Views

Author

Larry Reeves (larryr(AT)acm.org), May 24 2001

Keywords

Comments

This sequence differs from A029513 in that all least significant zeros are removed before concatenation.
No more terms < 10^7. [Lars Blomberg, Oct 25 2011]

Examples

			See A061931 for example.

Links

Crossrefs

Cf. A029447-A029470, A029471-A029494, A029495-A029518, A029519-A029542, A061931-A061954, A061955-A061978.

Programs

  • Mathematica
    b = 20; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[c, IntegerDigits[IntegerReverse[#, b], b]], b], #] &] (* Robert Price, Mar 08 2020 *)

Extensions

Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002; Aug 25, 2002
a(28)-a(29) from Lars Blomberg, Oct 25 2011

A061951 Numbers n such that n divides the (right) concatenation of all numbers <= n written in base 22 (most significant digit on right).

Original entry on oeis.org

1, 2, 3, 6, 7, 9, 11, 14, 18, 21, 63, 101, 119, 134, 177, 196, 255, 318, 360, 483, 1092, 1953, 2793, 3453, 4302, 5445, 5687, 5955, 6027, 6077, 9483, 16521, 23026, 28095, 76139, 125199, 135082, 209601, 518238, 573590, 993891, 1921962, 3467968, 4426863, 4842350
Offset: 1

Views

Author

Larry Reeves (larryr(AT)acm.org), May 24 2001

Keywords

Comments

This sequence differs from A029515 in that all least significant zeros are removed before concatenation.

Examples

			See A061931 for example.

Links

Crossrefs

Cf. A029447-A029470, A029471-A029494, A029495-A029518, A029519-A029542, A061931-A061954, A061955-A061978.

Programs

  • Mathematica
    b = 22; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[c, IntegerDigits[IntegerReverse[#, b], b]], b], #] &] (* Robert Price, Mar 08 2020 *)

Extensions

Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002

A061963 Numbers n such that n divides the (left) concatenation of all numbers <= n written in base 10 (most significant digit on right).

Original entry on oeis.org

1, 3, 9, 189, 753, 987, 6739, 10953, 51963, 171897, 224081, 635031, 1135001, 4437459
Offset: 1

Views

Author

Larry Reeves (larryr(AT)acm.org), May 24 2001

Keywords

Comments

This sequence differs from A029527 in that all least significant zeros are kept during concatenation.
Left concatenation, reverse order (i.e., digit-wise reversal of the concatenation 123...n), as in A138793.
No more terms < 10^7.
All terms must be odd.

Examples

			n = 13 is not a term since 31211101987654321 is not divisible by 13. (Note that the order of the digits of 13, 12 and 10 is reversed.)
See A061955 for further examples.

Links

Crossrefs

Cf. A029447-A029470, A029471-A029494, A029495-A029518, A029519-A029542, A061931-A061954, A061955-A061978.
Cf. A138793.

Programs

  • Mathematica
    k = 2; lst = {}; rid = 1; While[k < 1001, exp = Floor[ Log10[rid]] + 1 + If[Mod[k, 10] == 1, IntegerExponent[k - 1, 10], 0]; rid = rid + FromDigits@ Reverse@ IntegerDigits@ k*(10^exp); If[ Mod[rid, k] == 0, Print@ k; AppendTo[lst,k]]; k++]; lst (* and to test any single value n *) fQ[n_] := Mod[ FromDigits@ Reverse@ Flatten@ IntegerDigits@ Range@ n, n] == 0 (* Robert G. Wilson v, Sep 12 2011 *)
Select[Range[5*10^6],Divisible[FromDigits[Reverse[Flatten[ IntegerDigits/@ Range[ #]]]], #]&] (* Harvey P. Dale, Apr 10 2017 *)
  • PARI
    isok(n) = my(s = ""); forstep (k=n, 1, -1, sk = digits(k); forstep (j=#sk, 1, -1, s = concat(s, sk[j]))); (eval(s) % n) == 0; \\ Michel Marcus, Jan 28 2017

Extensions

Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002
a(12)-a(14) from Lars Blomberg, Aug 19 2011

A029449 Numbers k that divide the (right) concatenation of all numbers <= k written in base 4 (most significant digit on left).

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 12, 14, 16, 18, 21, 24, 26, 28, 32, 36, 42, 48, 52, 56, 58, 63, 64, 72, 84, 96, 108, 126, 128, 144, 147, 168, 189, 192, 216, 252, 256, 276, 328, 362, 384, 456, 492, 512, 656, 768, 896, 904, 984, 1024, 1116, 1152, 1211, 1251, 1344, 1536, 1736
Offset: 1

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Cf. A007090.
Cf. A029447-A029470, A029471-A029494, A029495-A029518, A029519-A029542, A061931-A061954, A061955-A061978.

Programs

  • Mathematica
    b = 4; c = {}; Select[Range[10^5], Divisible[FromDigits[c = Join[c, IntegerDigits[#, b]], b], #] &] (* Robert Price, Mar 10 2020 *)

A029451 Numbers k that divide the (right) concatenation of all numbers <= k written in base 6 (most significant digit on left).

Original entry on oeis.org

1, 2, 3, 5, 6, 9, 10, 12, 15, 18, 20, 22, 25, 30, 36, 40, 45, 50, 54, 60, 68, 72, 75, 90, 100, 103, 108, 116, 120, 132, 135, 150, 180, 200, 216, 225, 226, 240, 252, 270, 274, 280, 285, 300, 308, 315, 324, 336, 350, 360, 378, 400, 405, 420, 432, 450, 456, 504
Offset: 1

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Cf. A007092.
Cf. A029447-A029470, A029471-A029494, A029495-A029518, A029519-A029542, A061931-A061954, A061955-A061978.

Programs

  • Mathematica
    b = 6; c = {}; Select[Range[10^5], Divisible[FromDigits[c = Join[c, IntegerDigits[#, b]], b], #] &] (* Robert Price, Mar 11 2020 *)

A029452 Numbers k that divide the (right) concatenation of all numbers <= k written in base 7 (most significant digit on left).

Original entry on oeis.org

1, 3, 7, 12, 21, 28, 44, 49, 60, 61, 63, 81, 84, 91, 97, 108, 140, 147, 180, 189, 196, 204, 212, 243, 252, 303, 308, 324, 343, 349, 376, 392, 441, 504, 831, 1029, 1057, 1176, 1561, 2401, 2744, 3101, 4312, 5096, 6027, 7203, 8232, 10339, 11669, 12936, 13755
Offset: 1

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Cf. A029447-A029470, A029471-A029494, A029495-A029518, A029519-A029542, A061931-A061954, A061955-A061978.

Programs

  • Mathematica
    b = 7; c = {}; Select[Range[10^5], Divisible[FromDigits[c = Join[c, IntegerDigits[#, b]], b], #] &] (* Robert Price, Mar 11 2020 *)

Extensions

More terms from David W. Wilson

A029453 Numbers k that divide the (right) concatenation of all numbers <= k written in base 8 (most significant digit on left).

Original entry on oeis.org

1, 2, 4, 6, 7, 8, 12, 13, 14, 15, 16, 21, 24, 28, 32, 35, 39, 42, 48, 49, 56, 64, 70, 98, 106, 112, 128, 147, 164, 196, 224, 231, 256, 289, 392, 448, 490, 512, 545, 560, 608, 640, 665, 688, 784, 872, 889, 896, 980, 1024, 1064, 1120, 1280, 1520, 1526, 1568
Offset: 1

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Cf. A007094.
Cf. A029447-A029470, A029471-A029494, A029495-A029518, A029519-A029542, A061931-A061954, A061955-A061978.

Programs

  • Mathematica
    b = 8; c = {}; Select[Range[10^5], Divisible[FromDigits[c = Join[c, IntegerDigits[#, b]], b], #] &] (* Robert Price, Mar 11 2020 *)

A029456 Numbers k that divide the (right) concatenation of all numbers <= k written in base 11 (most significant digit on left).

Original entry on oeis.org

1, 5, 11, 20, 25, 44, 55, 100, 121, 220, 275, 281, 484, 508, 605, 748, 1012, 1100, 1331, 1496, 1573, 1595, 1768, 2200, 3016, 3025, 3400, 4825, 4840, 6655, 7480, 9320, 9515, 10648, 11320, 12760, 14641, 15125, 15400, 15507, 16335, 16456, 17000, 17215
Offset: 1

Views

Author

Olivier Gérard

Keywords

Links

Crossrefs

Cf. A029447-A029470, A029471-A029494, A029495-A029518, A029519-A029542, A061931-A061954, A061955-A061978.

Programs

  • Mathematica
    b = 11; c = {}; Select[Range[10^5], Divisible[FromDigits[c = Join[c, IntegerDigits[#, b]], b], #] &] (* Robert Price, Mar 11 2020 *)

Extensions

More terms from David W. Wilson
Previous Showing 21-30 of 142 results. Next

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