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 141 results. Next

A029447 Numbers k that divide the (right) concatenation of all numbers <= k written in base 2 (most significant digit on left).

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 16, 26, 32, 38, 40, 46, 64, 96, 128, 138, 192, 228, 256, 512, 640, 1024, 2048, 4096, 4192, 4766, 4790, 5142, 5952, 6144, 6866, 8122, 8192, 8448, 10240, 11283, 11392, 12288, 14780, 15360, 15744, 16384, 17408, 20841, 20866, 32768, 58496, 59104
Offset: 1

Views

Author

Olivier Gérard

Keywords

Comments

All powers of 2 are in the sequence. - Chai Wah Wu, Nov 10 2014
Numbers k that divide A047778(k). - Michel Marcus, Nov 11 2014

Examples

			3 is in the sequence because the concatenation is 1 10 11, binary expansion of 27, that is divisible by 3.

Links

Crossrefs

Cf. A007088, A047778.
Cf. A029447-A029470, A029471-A029494, A029495-A029518, A029519-A029542, A061931-A061954, A061955-A061978.

Programs

  • Mathematica
    Select[Range[2^13], Mod[FromDigits[Flatten[IntegerDigits[#, 2] & /@ Range@ #], 2], #] == 0 &] (* Michael De Vlieger, Aug 29 2015 *)
  • PARI
    lista(nn) = {vs = []; for (n=1, nn, vs = concat(vs, binary(n)); val = subst(Pol(vs), x, 2); if (val % n == 0, print1(n, ", ")););} \\ Michel Marcus, Nov 11 2014

Extensions

More terms from Scott Lindhurst (ScottL(AT)alumni.princeton.edu)
More terms from David W. Wilson
a(47)-a(49) from Chai Wah Wu, Nov 10 2014

A029542 Numbers k such that k divides the (left) concatenation of all numbers <= k written in base 25 (most significant digit on right and removing all least significant zeros before concatenation).

Original entry on oeis.org

1, 3, 9, 21, 27, 48, 144, 352, 361, 4672, 5904, 7392, 15323, 25488, 32096, 55491, 71712, 89259, 101437, 139776, 752011, 2215168, 5082544, 6766761
Offset: 1

Views

Author

Olivier Gérard

Keywords

Comments

This sequence differs from A061978 in that all least significant zeros are removed before concatenation.
No more terms < 10^7. - Lars Blomberg, Oct 01 2011

Examples

			See A029519 for example.

Links

Crossrefs

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

Programs

  • Mathematica
    b = 25; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[IntegerDigits[ IntegerReverse[ #, b], b], c], b], #] &] (* Robert Price, Mar 13 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), Jun 04 2001
a(21)-a(24) from Lars Blomberg, Oct 01 2011

A061931 Numbers n such that n divides the (right) concatenation of all numbers <= n written in base 2 (most significant digit on right).

Original entry on oeis.org

1, 3, 7, 39, 63, 523, 4983, 25007, 892217, 1142775, 1381311, 1751751
Offset: 1

Views

Author

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

Keywords

Comments

This sequence differs from A029495 in that all least significant zeros are removed before concatenation.
No more terms < 10^7. [Lars Blomberg, Oct 17 2011]

Examples

			1234567 -> (1)(01)(11)(001)(101)(011)(111) base 2 -> 1111110111111 base 2 = 8127 and 7 divides 8127.

Links

Crossrefs

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

Programs

  • Mathematica
    b = 2; c = {}; Select[Range[10^4], Divisible[FromDigits[
c = Join[c, IntegerDigits[IntegerReverse[#, b], b]], b], #] &] (* Robert Price, Mar 07 2020 *)
  • Python
    def agen():
  k, concat = 1, 1
  while True:
    if concat%k == 0: yield k
    revbink_even = (bin(k+1)[2:])[::-1]
    revbink_odd = '1' + revbink_even[1:]
    add_str = revbink_even[revbink_even.index('1'):] + revbink_odd
    concat = (concat << len(add_str)) + int(add_str, 2)
    k += 2
g = agen()
print([next(g) for i in range(8)]) # Michael S. Branicky, Jan 03 2021

Extensions

Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002
a(9)-a(12) from Lars Blomberg, Oct 17 2011

A061978 Numbers n such that n divides the (left) concatenation of all numbers <= n written in base 25 (most significant digit on right).

Original entry on oeis.org

1, 3, 9, 21, 33, 57, 96, 864, 1033, 1661, 6449, 6624, 10464, 68249, 81664, 108981, 164384, 167571, 234311, 2420409, 5490464
Offset: 1

Views

Author

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

Keywords

Comments

This sequence differs from A029542 in that all least significant zeros are kept during concatenation.
No more terms < 7*10^6.

Examples

			See A061955 for example.

Links

Crossrefs

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

Programs

  • Mathematica
    b = 25; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[Reverse[IntegerDigits[#, b]], c], b], #] &] (* Robert Price, Mar 09 2020 *)

Extensions

Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002
a(20)-a(21) from Lars Blomberg, Jul 22 2011

A029470 Numbers k that divide the (right) concatenation of all numbers <= k written in base 25 (most significant digit on left).

Original entry on oeis.org

1, 3, 5, 9, 15, 21, 25, 35, 64, 75, 125, 192, 320, 345, 375, 625, 675, 825, 875, 945, 960, 1117, 1125, 1155, 1255, 1344, 1375, 1485, 1575, 1600, 1728, 1875, 1925, 2240, 2475, 2625, 2880, 3125, 3375, 3465, 3520, 4032, 4065, 4125, 4375, 4725, 4800, 5625, 5775
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 = 25; c = {}; Select[Range[10^5], Divisible[FromDigits[c = Join[c, IntegerDigits[#, b]], b], #] &] (* Robert Price, Mar 11 2020 *)

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), May 02 2001

A029471 Numbers k that divide the (left) concatenation of all numbers <= k written in base 2 (most significant digit on left).

Original entry on oeis.org

1, 85, 145, 245, 1189, 356717, 19590671, 35741759, 791822369, 25313027035
Offset: 1

Views

Author

Olivier Gérard

Keywords

Comments

No other terms below 3*10^10.

Links

Crossrefs

Cf. A007088.
Cf. A029447-A029470, A029471-A029494, A029495-A029518, A029519-A029542, A061931-A061954, A061955-A061978.

Programs

  • Mathematica
    b = 2; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[IntegerDigits[#, b], c], b], #] &] (* Robert Price, Mar 12 2020 *)
  • Python
    from itertools import count
def a029471():
    total = 0
    power_of_two = 1
    index_of_two = 0
    length_of_string = 0
    for n in count(1):
        total += (n<Christian Perfect, Feb 07 2014
  • Python
    def concat_mod(base, k, mod): ...  # See A029479
for k in range(1, 3*10**10):
  if concat_mod(2, k, k) == 0: print(k) # Jason Yuen, Mar 24 2024

Extensions

One more term from Larry Reeves (larryr(AT)acm.org), Dec 03 2001
Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002
a(7)-a(8) from Max Alekseyev, May 12 2011
a(9)-a(10) from Jason Yuen, Mar 24 2024

A029494 Numbers k that divide the (left) concatenation of all numbers <= k written in base 25 (most significant digit on left).

Original entry on oeis.org

1, 3, 9, 21, 39, 71, 101, 111, 128, 239, 251, 384, 401, 419, 521, 1152, 1664, 4992, 14976, 21617, 23296, 29952, 34437, 36608, 45312, 51183, 92928, 117481, 191232, 225043, 255309, 742144, 910592, 1374464, 4074467, 5427968, 10461747, 10528128, 10897536, 14721408, 15387264, 15529344, 18626688, 20796849, 27863424, 28862509, 32013423, 41722496, 47329152, 52894873, 64367901, 66678144, 68195712, 77870208
Offset: 1

Views

Author

Olivier Gérard

Keywords

Comments

a(73) > 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 = 25; 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(32)-a(54) from Max Alekseyev, May 16 2011

A029495 Numbers k such that k divides the (right) concatenation of all numbers <= k written in base 2 (most significant digit on right).

Original entry on oeis.org

1, 5, 337
Offset: 1

Views

Author

Olivier Gérard

Keywords

Comments

This sequence differs from A061931 in that all least significant zeros are kept during concatenation.
No more terms < 10^7. - Lars Blomberg, Oct 01 2011

Examples

			12345 -> (1)(01)(11)(001)(101) base 2 -> 10111001101 base 2 = 1485 and 5 divides 1485.

Links

Crossrefs

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

Programs

  • Mathematica
    b = 2; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[c, Reverse[IntegerDigits[#, b]]], b], #] &] (* Robert Price, Mar 12 2020 *)
  • PARI
    is(n) = my(t=[]); for(k=1, n, t=concat(t, Vecrev(binary(k)))); if(Mod(subst(Pol(t), x, 2), n)==0, return(1), return(0)) \\ Felix Fröhlich, Jul 06 2017

Extensions

Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002
Additional comments, more terms and example from Larry Reeves (larryr(AT)acm.org), May 25 2001

A029518 Numbers k such that k divides the (right) concatenation of all numbers <= k written in base 25 (most significant digit on right).

Original entry on oeis.org

1, 3, 5, 9, 15, 21, 39, 83, 96, 288, 303, 864, 1824, 2421, 2496, 2592, 2817, 3328, 6299, 9440, 13632, 18592, 26049, 64857, 69696, 71904, 79872, 94848, 120384, 258111, 287232, 319319, 476736, 524992, 706368, 904281, 1817583, 2003520, 3156192, 4479904, 7460741
Offset: 1

Views

Author

Olivier Gérard

Keywords

Comments

This sequence differs from A061954 in that all least significant zeros are kept during concatenation.

Examples

			See A029495 for example.

Links

Crossrefs

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

Programs

  • Mathematica
    b = 25; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[c, Reverse[IntegerDigits[#, b]]], b], #] &] (* Robert Price, Mar 13 2020 *)
  • PARI
    lista(nn, m=25) = my(s, t); for(k=1, nn, s=k; while(s, t=t*m+s%m; s\=m); if(t%k==0, print1(k, ", "))); \\ Jinyuan Wang, Dec 05 2020

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), May 25 2001
Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002
a(33) and beyond from Lars Blomberg, Oct 14 2011

A029519 Numbers k such that k divides the (left) concatenation of all numbers <= k written in base 2 (most significant digit on right and removing all least significant zeros before concatenation).

Original entry on oeis.org

1, 3, 7, 17, 27, 63, 92883, 1556671
Offset: 1

Views

Author

Olivier Gérard

Keywords

Comments

This sequence differs from A061955 in that all least significant zeros are removed before concatenation.
No more terms < 10^7. - Lars Blomberg, Aug 31 2011

Examples

			7 is in the sequence as the left concatenation of numbers <= 7 is 7654321 which gives 7654321 -> (111)(011)(101)(001)(11)(01)(1) base 2 -> 1111110111111_2 = 8127, and 7 divides 8127.

Links

Crossrefs

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

Programs

  • J
    mkcat =: 13 : 'y +. #. ; #:&.> |.&.#:&.> |. >:i. y'
(#~ (= mkcat"0)) >:i. 100x NB. Stephen Makdisi, May 03 2018
  • Mathematica
    b = 2; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[IntegerDigits[IntegerReverse[#, b], b], c], b], #] &] (* Robert Price, Mar 13 2020 *)

Extensions

Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002
Additional comments and example from Larry Reeves (larryr(AT)acm.org), May 25 2001
Terms verified by Rick L. Shepherd, Feb 24 2009
1 more term from Sean A. Irvine, Oct 04 2009
Showing 1-10 of 141 results. Next

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

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