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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A029480 Numbers k that divide the (left) concatenation of all numbers <= k written in base 11 (most significant digit on left).

Original entry on oeis.org

1, 5, 15, 24, 25, 40, 75, 104, 120, 200, 271, 600, 696, 744, 1571, 1779, 2425, 3920, 4592, 7213, 9615, 11417, 11681, 11805, 14928, 18000, 18800, 22597, 54000, 82640, 119760, 177000, 218600, 461625, 547592, 547640, 561975, 641800, 861400, 1133368, 1575435, 2628185, 3114965, 3992975, 4455400, 5902975, 6404952, 17862425, 24200673, 24629515, 26758880, 29749915, 29831776, 42704185, 46355725, 53164695, 54814075, 69283747, 85552800
Offset: 1

Views

Author

Olivier Gérard

Keywords

Comments

a(89) > 3*10^10. - Jason Yuen, May 31 2024

Links

Crossrefs

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

Programs

  • Mathematica
    b = 11; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[IntegerDigits[#, b], c], b], #] &] (* Robert Price, Mar 12 2020 *)

Extensions

More terms from Andrew Gacek (andrew(AT)dgi.net), Feb 20 2000
More terms from Larry Reeves (larryr(AT)acm.org), May 24 2001
Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002
a(41)-a(59) from Max Alekseyev, May 16 2011

A029482 Numbers k that divide the (left) concatenation of all numbers <= k written in base 13 (most significant digit on left).

Original entry on oeis.org

1, 3, 9, 15, 21, 35, 53, 64, 105, 192, 320, 448, 576, 960, 1344, 2583, 2611, 2688, 4480, 5760, 8064, 8865, 12160, 13440, 23168, 28413, 131727, 201349, 654231, 901299, 1121799, 2629184, 11874240, 13712832, 35644608, 68560525, 76680065, 79404800, 97064075
Offset: 1

Views

Author

Olivier Gérard

Keywords

Comments

a(84) > 3*10^10. - Jason Yuen, May 31 2024

Links

Crossrefs

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

Programs

  • Mathematica
    b = 13; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[IntegerDigits[#, b], c], b], #] &] (* Robert Price, Mar 12 2020 *)

Extensions

More terms from Andrew Gacek (andrew(AT)dgi.net), Feb 20 2000
More terms from Larry Reeves (larryr(AT)acm.org), May 24 2001
Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002
a(29)-a(39) from Max Alekseyev, May 16 2011

A029484 Numbers k that divide the (left) concatenation of all numbers <= k written in base 15 (most significant digit on left).

Original entry on oeis.org

1, 7, 32, 49, 61, 91, 169, 224, 791, 1568, 10304, 34112, 160832, 733376, 966721, 1127392, 4197571, 10914848, 13250272, 15000608, 62776133, 70412363, 82053664, 138391456, 198795233, 211659392, 272510336, 484441216, 1448538133, 1846451173, 2444373281, 2681439341, 11942145152, 22206078181, 25210297984
Offset: 1

Views

Author

Olivier Gérard

Keywords

Comments

No other terms below 3*10^10.
No multiple of 3 or 5 can be in this sequence, since the numbers resulting from these concatenations are all congruent to 1 mod 15. - Alonso del Arte, Sep 16 2016

Examples

			In base 15, 7654321 is 84557956 in decimal, and we verify that this is a multiple of 7, as 84557956/7 = 12079708. Hence 7 is in the sequence.
87654321 base 15 is 1451432956 and 1451432956/8 = 181429119.5. Hence 8 is not in the sequence.

Links

Crossrefs

Cf. A029447-A029470 (in particular, A029460), A029471-A029494, A029495-A029518, A029519-A029542, A061931-A061954, A061955-A061978.

Programs

  • Mathematica
    Select[Range[10^3], Divisible[FromDigits[#, 15] &@ Flatten@ Reverse@ IntegerDigits[Range@ #, 15], #] &] (* Michael De Vlieger, Sep 16 2016 *)

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Jun 01 2001
Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002
a(14)-a(23) from Max Alekseyev, May 15 2011
a(24)-a(35) from Jason Yuen, Jun 05 2024

A029485 Numbers k that divide the (left) concatenation of all numbers <= k written in base 16 (most significant digit on left).

Original entry on oeis.org

1, 3, 5, 9, 15, 25, 75, 257, 321, 435, 795, 1285, 2313, 8523, 39759, 60855, 91209, 247875, 251385, 2695341, 5095725, 9529505, 12179807, 12341125, 57965805, 1380206235, 15616692345, 22548618825, 26313971049
Offset: 1

Views

Author

Olivier Gérard

Keywords

Comments

No other terms below 3*10^10.

Examples

			For k=3, we have 321_16 which is 801, and 801 = 3*267.

Links

Crossrefs

Cf. A029447-A029470, A029471-A029484, A029486-A029494, A029495-A029518, A029519-A029542, A061931-A061954, A061955-A061978.

Programs

  • Mathematica
    b = 16; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[IntegerDigits[#, b], c], b], #] &] (* Robert Price, Mar 12 2020 *)

Extensions

More terms from Andrew Gacek (andrew(AT)dgi.net), Feb 21 2000
More terms from Larry Reeves (larryr(AT)acm.org), Aug 27 2001
Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002
a(20)-a(25) from Max Alekseyev, May 15 2011
a(26)-a(29) from Jason Yuen, Jun 29 2024

A029487 Numbers k that divide the (left) concatenation of all numbers <= k written in base 18 (most significant digit on left).

Original entry on oeis.org

1, 17, 49, 73, 289, 307, 1297, 3013, 8959, 664831, 1399549, 5122561, 8515193, 11012719, 65998063, 145256891, 294363959, 734746001, 1255837139, 1454498597, 5287956641
Offset: 1

Views

Author

Olivier Gérard

Keywords

Comments

No other terms below 3*10^10.

Links

Crossrefs

Cf. A029447-A029470, A029471-A029486, A029488-A029494, A029495-A029518, A029519-A029542, A061931-A061954, A061955-A061978.

Programs

  • Mathematica
    b = 18; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[IntegerDigits[#, b], c], b], #] &] (* Robert Price, Mar 12 2020 *)

Extensions

More terms from Andrew Gacek (andrew(AT)dgi.net), Feb 21 2000
a(9) corrected by Larry Reeves (larryr(AT)acm.org), Jan 14 2002
Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002
a(10)-a(15) from Max Alekseyev, May 15 2011
a(16)-a(21) from Jason Yuen, Jun 29 2024

A029490 Numbers k that divide the (left) concatenation of all numbers <= k written in base 21 (most significant digit on left).

Original entry on oeis.org

1, 5, 25, 43, 55, 128, 275, 1280, 2816, 5888, 6400, 12800, 28160, 33413, 37376, 129919, 140800, 286025, 352000, 990845, 1050880, 1773725, 2848000, 3581033, 4343680, 4428160, 5624960, 6732160, 7553920, 8497280, 9249995, 9872000, 10938752, 11426176, 14558575, 14569600, 15368320, 18998705, 19312000, 21362275, 24208000, 24934855, 27632000, 32432000, 37022605, 43193216, 51382265, 53717375, 81016375
Offset: 1

Views

Author

Olivier Gérard

Keywords

Comments

a(62) > 3*10^10. - Jason Yuen, Jun 29 2024

Links

Crossrefs

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

Programs

  • Mathematica
    b = 21; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[IntegerDigits[#, b], c], b], #] &] (* Robert Price, Mar 12 2020 *)

Extensions

More terms from Andrew Gacek (andrew(AT)dgi.net), Feb 21 2000
More terms from Larry Reeves (larryr(AT)acm.org), May 24 2001
Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002
a(20)-a(49) from Max Alekseyev, May 15 2011

A029491 Numbers k that divide the (left) concatenation of all numbers <= k written in base 22 (most significant digit on left).

Original entry on oeis.org

1, 3, 7, 9, 21, 49, 59, 67, 89, 147, 353, 1057, 1773, 4711, 6943, 29691, 40719, 51309, 57533, 116881, 155769, 178311, 207123, 9111701, 9636685, 10090955, 14397327, 21361545, 23023665, 50170565, 55533513, 72268665, 316155105, 635174505, 780744111, 932896685
Offset: 1

Views

Author

Olivier Gérard

Keywords

Comments

a(52) > 3*10^10. - Jason Yuen, Jun 30 2024

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[IntegerDigits[#, b], c], b], #] &] (* Robert Price, Mar 12 2020 *)

Extensions

More terms from Andrew Gacek (andrew(AT)dgi.net), Feb 21 2000
More terms from Larry Reeves (larryr(AT)acm.org), Jun 01 2001
Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002
a(24)-a(32) from Max Alekseyev, May 15 2011

A029492 Numbers k that divide the (left) concatenation of all numbers <= k written in base 23 (most significant digit on left).

Original entry on oeis.org

1, 11, 27, 33, 48, 93, 99, 121, 144, 176, 297, 304, 363, 432, 461, 528, 583, 1936, 2267, 2915, 5808, 12031, 22496, 26983, 31328, 33913, 63861, 81312, 93984, 105888, 108803, 143264, 477103, 1287968, 3511904, 3620768, 7292912, 31740567, 62025997, 63469123
Offset: 1

Views

Author

Olivier Gérard

Keywords

Comments

a(54) > 3*10^10. - Jason Yuen, Jun 30 2024

Links

Crossrefs

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

Programs

  • Mathematica
    b = 23; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[IntegerDigits[#, b], c], b], #] &] (* Robert Price, Mar 12 2020 *)

Extensions

More terms from Andrew Gacek (andrew(AT)dgi.net), Feb 21 2000
More terms from Larry Reeves (larryr(AT)acm.org), May 24 2001
Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002
a(34)-a(40) from Max Alekseyev, May 15 2011

A029496 Numbers n such that n divides the (right) concatenation of all numbers <= n written in base 3 (most significant digit on right).

Original entry on oeis.org

1, 7, 8, 112, 424, 595, 1997, 2336, 2455, 33265, 2475701, 9363208, 15402464
Offset: 1

Views

Author

Olivier Gérard

Keywords

Comments

This sequence differs from A061932 in that all least significant zeros are kept during concatenation.
No more terms < 10^7. [Lars Blomberg, Oct 02 2011]

Examples

			See A029495 for example.

Links

Crossrefs

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

Programs

  • Mathematica
    b = 3; c = {}; Select[Range[10^4], Divisible[FromDigits[
c = Join[c, Reverse[IntegerDigits[#, b]]], b], #] &] (* Robert Price, Mar 12 2020 *)

Extensions

Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002
Additional comments from Larry Reeves (larryr(AT)acm.org), May 25 2001
a(10) from Larry Reeves, Jan 16 2002
a(11)-a(12) from Lars Blomberg, Oct 02 2011
a(13) from Chai Wah Wu, Jul 28 2020

A029497 Numbers k such that k divides the (right) concatenation of all numbers <= k written in base 4 (most significant digit on right).

Original entry on oeis.org

1, 2, 3, 11, 207, 1239, 7947, 9233, 49883, 118669, 315629, 2640670
Offset: 1

Views

Author

Olivier Gérard

Keywords

Comments

This sequence differs from A061933 in that all least significant zeros are kept during concatenation.
a(13) exceeds 10000000. - Sean A. Irvine, Sep 01 2009

Examples

			See A029495 for example.

Links

Crossrefs

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

Programs

  • Mathematica
    b = 4; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[c, Reverse[IntegerDigits[#, b]]], b], #] &] (* Robert Price, Mar 12 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(12) from Sean A. Irvine, Sep 01 2009
Previous Showing 41-50 of 142 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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