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 21 results. Next

A182232 Numbers that are palindromic in bases 2 and 5.

Original entry on oeis.org

0, 1, 3, 31, 93, 119, 2709, 38937, 520831, 682341, 340134981, 7609865031, 17935304097, 26777829859, 169179279801, 567897922593, 286118927218753, 2996750083037781, 4738749440161121, 6299497017331917, 8829547069230943
Offset: 1

Views

Author

Alex Ratushnyak, Apr 19 2012

Keywords

Comments

Intersection of A006995 and A029952. - Michel Marcus, Oct 08 2014

Examples

			2709 base 2 = 101010010101 and 2709 base 5 = 41314.

Links

Crossrefs

Cf. A060792, A097856.

Programs

  • Mathematica
    b1 = 2; b2 = 5; lst = {}; Do[d1 = IntegerDigits[n, b1]; d2 = IntegerDigits[n, b2]; If[d1 == Reverse[d1] && d2 == Reverse[d2], AppendTo[lst, n]], {n, 1000000}]; lst (* T. D. Noe, Apr 19 2012 *)

Extensions

Term 0 prepended by Robert G. Wilson v, Oct 08 2014
a(12)-a(16) from Robert G. Wilson v, Oct 11 2014
a(17)-a(21) and b-file from Ray Chandler, Oct 24 2014

A182233 Numbers that are palindromic in bases 2 and 6.

Original entry on oeis.org

0, 1, 3, 5, 7, 21, 129, 427, 693, 819, 3999, 4257, 4593, 28539, 66433, 85093, 148617, 151497, 153513, 180213, 425971, 1040319, 1093281, 1508381, 1632995, 1974031, 1986127, 30522135, 30643095, 208080483, 1894216583, 6662648163, 8632935681
Offset: 1

Views

Author

Alex Ratushnyak, Apr 19 2012

Keywords

Comments

Intersection of A006995 and A029953. - Michel Marcus, Oct 09 2014

Examples

			85093 base 2 = 10100110001100101 and 85093 base 6 = 1453541.

Links

Crossrefs

Cf. A006995 (base 2), A029953 (base 6).
Cf. A060792 (base 2 and 3), A097856 (base 2 and 4).

Programs

  • Mathematica
    b1 = 2; b2 = 6; lst = {}; Do[d1 = IntegerDigits[n, b1]; d2 = IntegerDigits[n, b2]; If[d1 == Reverse[d1] && d2 == Reverse[d2], AppendTo[lst, n]], {n, 2000000}]; lst (* T. D. Noe, Apr 19 2012 *)
  • PARI
    isok(n) = (d2=digits(n, 2)) && (d2==Vecrev(d2)) && (d6=digits(n, 6)) && (d6==Vecrev(d6)); \\ Michel Marcus, Oct 27 2014

Extensions

a(28)-a(33) and b-file from Ray Chandler, Oct 27 2014

A182234 Numbers that are palindromic in bases 2 and 7.

Original entry on oeis.org

0, 1, 3, 5, 85, 107, 257, 5049, 9201, 11253, 11757, 210099, 399171, 512607, 786435, 12916899, 19992857, 22468309, 1052109663, 15935958711, 24051338445, 37344016593, 71859215265, 72822171105, 1566399158893, 3425211644643
Offset: 1

Views

Author

Alex Ratushnyak, Apr 19 2012

Keywords

Comments

Intersection of A006995 and A029954. - Michel Marcus, Oct 09 2014

Examples

			786435 base 2 = 11000000000000000011 and 786435 base 7 = 6453546.

Links

Crossrefs

Cf. A006995 (base 2), A029954 (base 7).
Cf. A060792 (base 2 and 3), A097856 (base 2 and 4).

Programs

  • Mathematica
    b1 = 2; b2 = 7; lst = {}; Do[d1 = IntegerDigits[n, b1]; d2 = IntegerDigits[n, b2]; If[d1 == Reverse[d1] && d2 == Reverse[d2], AppendTo[lst, n]], {n, 1000000}]; lst (* T. D. Noe, Apr 19 2012 *)

Extensions

a(19)-a(28) from Donovan Johnson, Apr 27 2012
b-file to 31 terms from Ray Chandler, Oct 27 2014

A259380 Palindromic numbers in bases 2 and 8 written in base 10.

Original entry on oeis.org

0, 1, 3, 5, 7, 9, 27, 45, 63, 65, 73, 195, 219, 325, 341, 365, 381, 455, 471, 495, 511, 513, 585, 1539, 1755, 2565, 2709, 2925, 3069, 3591, 3735, 3951, 4095, 4097, 4161, 4617, 4681, 12291, 12483, 13851, 14043, 20485, 20613, 20805, 20933, 21525, 21653, 21845, 21973, 23085, 23213, 23405, 23533, 24125, 24253, 24445, 24573, 28679, 28807, 28999, 29127, 29719, 29847
Offset: 1

Views

Author

Eric A. Schmidt and Robert G. Wilson v, Jul 16 2015

Keywords

Examples

			2709 is in the sequence because 2709_10 = 5225_8 = 101010010101_2.

Links

Crossrefs

Cf. A048268, A060792, A097856, A097928, A182232, A259374, A097929, A182233, A259375, A259376,
A097930, A182234, A259377, A259378, A249156, A097931, A259380, A259381, A259382, A259383,
A259384, A099145, A259385, A259386, A259387, A259388, A259389, A259390, A099146, A007632,
A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968,
A029969, A029970, A029731, A097855, A250408, A250409, A250410, A250411, A099165, A250412.

Programs

  • Mathematica
    (* first load nthPalindromeBase from A002113 *) palQ[n_Integer, base_Integer] := Block[{}, Reverse[ idn = IntegerDigits[n, base]] == idn]; k = 0; lst = {}; While[k < 21000000, pp = nthPalindromeBase[k, 8]; If[palQ[pp, 2], AppendTo[lst, pp]; Print[pp]]; k++]; lst
b1=2; b2=8; lst={}; Do[d1=IntegerDigits[n, b1]; d2=IntegerDigits[n, b2]; If[d1==Reverse[d1]&&d2==Reverse[d2], AppendTo[lst, n]], {n, 0, 30000}]; lst (* Vincenzo Librandi, Jul 17 2015 *)

Formula

Intersection of A006995 and A029803.

A259374 Palindromic numbers in bases 3 and 5 written in base 10.

Original entry on oeis.org

0, 1, 2, 4, 26, 52, 1066, 1667, 2188, 32152, 67834, 423176, 437576, 14752936, 26513692, 27711772, 33274388, 320785556, 1065805109, 9012701786, 9256436186, 12814126552, 18814619428, 201241053056, 478999841578, 670919564984, 18432110906024, 158312796835916, 278737550525722
Offset: 1

Views

Author

Eric A. Schmidt and Robert G. Wilson v, Jul 14 2015

Keywords

Comments

0 is only 0 regardless of the base,
1 is only 1 regardless of the base,
2 on the other hand is also 10 in base 2, denoted as 10_2,
3 is 3 in all bases greater than 3, but is 11_2 and 10_3.

Examples

			52 is in the sequence because 52_10 = 202_5 = 1221_3.

Links

Crossrefs

Cf. A048268, A060792, A097856, A097928, A182232, A259374, A097929, A182233, A259375, A259376, A097930, A182234, A259377, A259378, A249156, A097931, A259380-A259384, A099145, A259385-A259390, A099146, A007632, A007633, A029961-A029964, A029804, A029965-A029970, A029731, A097855, A250408-A250411, A099165, A250412.

Programs

  • Mathematica
    (* first load nthPalindromeBase from A002113 *) palQ[n_Integer, base_Integer] := Block[{}, Reverse[ idn = IntegerDigits[n, base]] == idn]; k = 0; lst = {}; While[k < 21000000, pp = nthPalindromeBase[k, 5]; If[ palQ[pp, 3], AppendTo[lst, pp]; Print[pp]]; k++]; lst
b1=3; b2=5; lst={}; Do[d1=IntegerDigits[n, b1]; d2=IntegerDigits[n, b2]; If[d1==Reverse[d1]&&d2==Reverse[d2], AppendTo[lst, n]], {n, 0, 10000000}]; lst (* Vincenzo Librandi, Jul 15 2015 *)
  • Python
    def nextpal(n,b): # returns the palindromic successor of n in base b
    m, pl = n+1, 0
    while m > 0:
        m, pl = m//b, pl+1
    if n+1 == b**pl:
        pl = pl+1
    n = (n//(b**(pl//2))+1)//(b**(pl%2))
    m = n
    while n > 0:
        m, n = m*b+n%b, n//b
    return m
n, a3, a5 = 0, 0, 0
while n <= 20000:
    if a3 < a5:
        a3 = nextpal(a3,3)
    elif a5 < a3:
        a5 = nextpal(a5,5)
    else: # a3 == a5
        print(n,a3)
        a3, a5, n = nextpal(a3,3), nextpal(a5,5), n+1
# A.H.M. Smeets, Jun 03 2019

Formula

Intersection of A014190 and A029952.

A259375 Palindromic numbers in bases 3 and 6 written in base 10.

Original entry on oeis.org

0, 1, 2, 4, 28, 80, 160, 203, 560, 644, 910, 34216, 34972, 74647, 87763, 122420, 221068, 225064, 6731644, 6877120, 6927700, 7723642, 8128762, 8271430, 77894071, 78526951, 539212009, 28476193256, 200267707484, 200316968444, 201509576804, 201669082004, 231852949304, 232018753064, 232039258376, 333349186006, 2947903946317, 5816975658914, 5817003372578, 11610051837124, 27950430282103, 81041908142188
Offset: 1

Views

Author

Eric A. Schmidt and Robert G. Wilson v, Jul 14 2015

Keywords

Comments

Agrees with the number of minimal dominating sets of the halved cube graph Q_n/2 for at least n=1 to 5. - Eric W. Weisstein, Sep 06 2021

Examples

			28 is in the sequence because 28_10 = 44_6 = 1001_3.

Links

Crossrefs

Cf. A048268, A060792, A097856, A097928, A182232, A259374, A097929, A182233, A259375, A259376, A097930, A182234, A259377, A259378, A249156, A097931, A259380, A259381, A259382, A259383, A259384, A099145, A259385, A259386, A259387, A259388, A259389, A259390, A099146, A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968, A029969, A029970, A029731, A097855, A250408, A250409, A250410, A250411, A099165, A250412.

Programs

  • Mathematica
    (* first load nthPalindromeBase from A002113 *) palQ[n_Integer, base_Integer] := Block[{}, Reverse[ idn = IntegerDigits[n, base]] == idn]; k = 0; lst = {}; While[k < 21000000, pp = nthPalindromeBase[k, 6]; If[palQ[pp, 3], AppendTo[lst, pp]; Print[pp]]; k++]; lst
b1=3; b2=6; lst={}; Do[d1=IntegerDigits[n, b1]; d2=IntegerDigits[n, b2]; If[d1==Reverse[d1]&&d2==Reverse[d2], AppendTo[lst, n]], {n, 0, 10000000}]; lst (* Vincenzo Librandi, Jul 15 2015 *)

Formula

Intersection of A014190 and A029953.

A259376 Palindromic numbers in bases 4 and 6 written in base 10.

Original entry on oeis.org

0, 1, 2, 3, 5, 21, 55, 215, 819, 1885, 7373, 7517, 12691, 14539, 69313, 196606, 1856845, 3314083, 5494725, 33348861, 223892055, 231755895, 322509617, 3614009815, 4036503055, 4165108015, 9233901154, 9330794722, 12982275395, 107074105033, 186398221946, 270747359295, 401478741365, 1809863435625, 2281658774290, 11931403417210, 12761538567790, 12887266632430, 15822654274715, 30255762326713, 46164680151002, 323292550693473, 329536806222753
Offset: 1

Views

Author

Eric A. Schmidt and Robert G. Wilson v, Jul 15 2015

Keywords

Examples

			55 is in the sequence because 55_10 = 131_6 = 313_4.

Links

Crossrefs

Cf. A048268, A060792, A097856, A097928, A182232, A259374, A097929, A182233, A259375, A259376,
A097930, A182234, A259377, A259378, A249156, A097931, A259380, A259381, A259382, A259383,
A259384, A099145, A259385, A259386, A259387, A259388, A259389, A259390, A099146, A007632,
A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968,
A029969, A029970, A029731, A097855, A250408, A250409, A250410, A250411, A099165, A250412.

Programs

  • Mathematica
    (* first load nthPalindromeBase from A002113 *) palQ[n_Integer, base_Integer] := Block[{}, Reverse[ idn = IntegerDigits[n, base]] == idn]; k = 0; lst = {}; While[k < 21000000, pp = nthPalindromeBase[k, 6]; If[palQ[pp, 4], AppendTo[lst, pp]; Print[pp]]; k++]; lst

Formula

Intersection of A014190 and A029953.

A259377 Palindromic numbers in bases 3 and 7 written in base 10.

Original entry on oeis.org

0, 1, 2, 4, 8, 16, 40, 100, 121, 142, 164, 242, 328, 400, 1312, 8200, 9103, 14762, 54008, 76024, 108016, 112048, 233920, 532900, 639721, 741586, 2585488, 3316520, 11502842, 24919360, 35664908, 87001616, 184827640, 4346524576, 5642510512, 11641189600, 65304259157, 68095147754, 469837033600, 830172165614, 17136683996456, 21772277941544, 22666883572232, 45221839119556
Offset: 1

Views

Author

Eric A. Schmidt and Robert G. Wilson v, Jul 16 2015

Keywords

Examples

			142 is in the sequence because 142_10 = 262_7 = 12021_3.

Links

Crossrefs

Cf. A007632, A007633, A029731, A029804, A029961, A029962, A029963, A029964, A029965, A029966, A029967, A029968, A029969, A029970, A048268, A060792, A097855, A097856, A097928, A097929, A097930, A097931, A099145, A099146, A099165, A182232, A182233, A182234, A250408, A250409, A250410, A250411, A250412, A259374, A259375, A259376, A259377, A259378, A249156, A259380, A259381, A259382, A259383, A259384, A259385, A259386, A259387, A259388, A259389, A259390.

Programs

  • Mathematica
    (* first load nthPalindromeBase from A002113 *) palQ[n_Integer, base_Integer] := Block[{}, Reverse[ idn = IntegerDigits[n, base]] == idn]; k = 0; lst = {}; While[k < 21000000, pp = nthPalindromeBase[k, 7]; If[palQ[pp, 3], AppendTo[lst, pp]; Print[pp]]; k++]; lst
b1=3; b2=7; lst={};Do[d1=IntegerDigits[n, b1]; d2=IntegerDigits[n, b2]; If[d1==Reverse[d1] && d2==Reverse[d2], AppendTo[lst, n]], {n, 0, 10000000}]; lst (* Vincenzo Librandi, Jul 17 2015 *)

Formula

Intersection of A014190 and A029954.

A259378 Palindromic numbers in bases 4 and 7 written in base 10.

Original entry on oeis.org

0, 1, 2, 3, 5, 85, 150, 235, 257, 8802, 9958, 13655, 14811, 189806, 428585, 786435, 9262450, 31946605, 34179458, 387973685, 424623193, 430421657, 640680742, 742494286, 1692399385, 22182595205, 30592589645, 1103782149121, 1134972961921, 1871644872505, 2047644601565, 3205015384750, 3304611554563, 3628335729863, 4467627704385
Offset: 1

Views

Author

Eric A. Schmidt and Robert G. Wilson v, Jul 16 2015

Keywords

Examples

			85 is in the sequence because 85_10 = 151_7 = 1111_4.

Links

Crossrefs

Cf. A048268, A060792, A097856, A097928, A182232, A259374, A097929, A182233, A259375, A259376, A097930, A182234, A259377, A259378, A249156, A097931, A259380, A259381, A259382, A259383, A259384, A099145, A259385, A259386, A259387, A259388, A259389, A259390, A099146, A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968, A029969, A029970, A029731, A097855, A250408, A250409, A250410, A250411, A099165, A250412.

Programs

  • Mathematica
    (* first load nthPalindromeBase from A002113 *) palQ[n_Integer, base_Integer] := Block[{}, Reverse[ idn = IntegerDigits[n, base]] == idn]; k = 0; lst = {}; While[k < 21000000, pp = nthPalindromeBase[k, 7]; If[palQ[pp, 4], AppendTo[lst, pp]; Print[pp]]; k++]; lst
b1=4; b2=7; lst={}; Do[d1=IntegerDigits[n, b1]; d2=IntegerDigits[n, b2]; If[d1==Reverse[d1]&&d2==Reverse[d2], AppendTo[lst, n]], {n, 0, 10000000}]; lst (* Vincenzo Librandi, Jul 17 2015 *)

Formula

Intersection of A014192 and A029954.

A259382 Palindromic numbers in bases 4 and 8 written in base 10.

Original entry on oeis.org

0, 1, 2, 3, 5, 63, 65, 105, 130, 170, 195, 235, 325, 341, 357, 373, 4095, 4097, 4161, 4225, 4289, 6697, 6761, 6825, 6889, 8194, 8258, 8322, 8386, 10794, 10858, 10922, 10986, 12291, 12355, 12419, 12483, 14891, 14955, 15019, 15083, 20485, 20805, 21525, 21845
Offset: 1

Views

Author

Eric A. Schmidt and Robert G. Wilson v, Jul 16 2015

Keywords

Examples

			235 is in the sequence because 235_10 = 353_8 = 3223_4.

Links

Crossrefs

Cf. A048268, A060792, A097856, A097928, A182232, A259374, A097929, A182233, A259375, A259376, A097930, A182234, A259377, A259378, A249156, A097931, A259380, A259381, A259382, A259383, A259384, A099145, A259385, A259386, A259387, A259388, A259389, A259390, A099146, A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968, A029969, A029970, A029731, A097855, A250408, A250409, A250410, A250411, A099165, A250412.

Programs

  • Mathematica
    (* first load nthPalindromeBase from A002113 *) palQ[n_Integer, base_Integer] := Block[{}, Reverse[ idn = IntegerDigits[n, base]] == idn]; k = 0; lst = {}; While[k < 21000000, pp = nthPalindromeBase[k, 8]; If[palQ[pp, 4], AppendTo[lst, pp]; Print[pp]]; k++]; lst
b1=4; b2=8; lst={}; Do[d1=IntegerDigits[n, b1]; d2=IntegerDigits[n, b2]; If[d1==Reverse[d1]&&d2==Reverse[d2], AppendTo[lst, n]], {n, 0, 30000}]; lst (* Vincenzo Librandi, Jul 17 2015 *)

Formula

Intersection of A014192 and A029803.

Extensions

Corrected and extended by Giovanni Resta, Jul 16 2015
Showing 1-10 of 21 results. Next

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