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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A259384 Palindromic numbers in bases 6 and 8 written in base 10.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 7, 154, 178, 203, 5001, 7409, 315721, 567434, 1032507, 46823602, 56939099, 84572293, 119204743, 1420737297, 1830945641, 2115191225, 3286138051, 3292861699, 4061216947, 8094406311, 43253138565, 80375377033, 88574916241, 108218625313, 116606986537, 116755331881, 166787896538, 186431605610, 318743407660, 396619220597, 1756866976011, 4920262093249, 11760498311914, 15804478291811, 15813860880803, 24722285628901, 33004205249575, 55584258482529, 371039856325905, 401205063672537, 516268720555889
Offset: 1

Views

Author

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

Keywords

Examples

			178 is in the sequence because 178_10 = 262_8 = 454_6.

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, 6], AppendTo[lst, pp]; Print[pp]]; k++]; lst
b1=6; b2=8; 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 A029953 and A029803.

A259385 Palindromic numbers in bases 2 and 9 written in base 10.

Original entry on oeis.org

0, 1, 3, 5, 7, 127, 255, 273, 455, 6643, 17057, 19433, 19929, 42405, 1245161, 1405397, 1786971, 2122113, 3519339, 4210945, 67472641, 90352181, 133638015, 134978817, 271114881, 6080408749, 11022828069, 24523959661, 25636651261, 25726334461, 28829406059, 1030890430479, 1032991588623, 1085079274815, 1616662113341
Offset: 1

Views

Author

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

Keywords

Examples

			273 is in the sequence because 273_10 = 333_9 = 100010001_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, 9]; If[palQ[pp, 2], AppendTo[lst, pp]; Print[pp]]; k++]; lst
  • Python
    def nextpal(n, base): # m is the first palindrome successor of n in base base
    m, pl = n+1, 0
    while m > 0:
        m, pl = m//base, pl+1
    if n+1 == base**pl:
        pl = pl+1
    n = n//(base**(pl//2))+1
    m, n = n, n//(base**(pl%2))
    while n > 0:
        m, n = m*base+n%base, n//base
    return m
n, a2, a9 = 0, 0, 0
while n <= 30:
    if a2 < a9:
        a2 = nextpal(a2,2)
    elif a9 < a2:
        a9 = nextpal(a9, 9)
    else: # a2 == a9
        print(a2, end=",")
        a2, a9, n = nextpal(a2,2), nextpal(a9,9), n+1 # A.H.M. Smeets, Jun 03 2019

Formula

Intersection of A006995 and A029955.

A259386 Palindromic numbers in bases 3 and 9 written in base 10.

Original entry on oeis.org

0, 1, 2, 4, 8, 10, 20, 40, 80, 82, 91, 100, 164, 173, 182, 328, 364, 400, 656, 692, 728, 730, 820, 910, 1460, 1550, 1640, 2920, 3280, 3640, 5840, 6200, 6560, 6562, 6643, 6724, 7300, 7381, 7462, 8038, 8119, 8200, 13124, 13205, 13286, 13862, 13943, 14024, 14600, 14681, 14762, 26248, 26572, 26896, 29200, 29524, 29848, 32152, 32476, 32800, 52496, 52820, 53144, 55448, 55772, 56096, 58400, 58724, 59048, 59050, 59860, 60670, 65620, 66430, 67240, 72190, 73000, 73810
Offset: 1

Views

Author

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

Keywords

Examples

			40 is in the sequence because 40_10 = 44_9 = 1111_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, 9]; If[palQ[pp, 3], AppendTo[lst, pp]; Print[pp]]; k++]; lst
b1=3; b2=9; lst={}; Do[d1=IntegerDigits[n, b1]; d2=IntegerDigits[n, b2]; If[d1==Reverse[d1]&&d2==Reverse[d2], AppendTo[lst, n]], {n, 0, 80000}]; lst (* Vincenzo Librandi, Jul 17 2015 *)

Formula

Intersection of A014190 and A029955.

A259390 Palindromic numbers in bases 7 and 9 written in base 10.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 8, 40, 50, 100, 164, 200, 264, 300, 328, 400, 2000, 3550, 8200, 10252, 14510, 14762, 22800, 45600, 164900, 201720, 400200, 532900, 555013, 738100, 2756120, 2913368, 3344352, 3501600, 4084000, 12990350, 22674550, 194062432, 1684866370, 2225211080, 13575144288, 15127811455, 20404027400, 20537111057, 22668403353, 30862471355, 83714515310, 84668107250, 796259955485, 1202029647736, 2088800185930, 20268849562000
Offset: 1

Views

Author

Eric A. Schmidt and Robert G. Wilson v, Jul 17 2015

Keywords

Examples

			264 is in the sequence because 264_10 = 323_9 = 525_7.

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, 9]; If[palQ[pp, 7], AppendTo[lst, pp]; Print[pp]]; k++]; lst

Formula

Intersection of A029954 and A029955.

A259381 Palindromic numbers in bases 3 and 8 written in base 10.

Original entry on oeis.org

0, 1, 2, 4, 121, 130, 203, 316, 8578, 9490, 17492, 944035, 1141652, 1276916, 1554173, 58961443, 67470916, 4099065139, 5691134677, 81452592329, 81473867465, 419572845958, 21056462595764, 363376288168081
Offset: 1

Views

Author

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

Keywords

Examples

			121 is in the sequence because 121_10 = 171_8 = 11111_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, 8]; If[palQ[pp, 3], AppendTo[lst, pp]; Print[pp]]; k++]; lst
b1=3; b2=8; 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 A029803.

A259383 Palindromic numbers in bases 5 and 8 written in base 10.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 18, 36, 186, 438, 2268, 2709, 11898, 18076, 151596, 228222, 563786, 5359842, 32285433, 257161401, 551366532, 621319212, 716064597, 2459962002, 5018349804, 5067084204, 7300948726, 42360367356, 139853034114, 176616961826, 469606524278, 669367713609, 1274936571666, 1284108810066, 5809320306961, 8866678870082, 11073162740322, 14952142559323, 325005646077513
Offset: 1

Views

Author

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

Keywords

Examples

			186 is in the sequence because 186_10 = 272_8 = 1221_5.

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, 5], AppendTo[lst, pp]; Print[pp]]; k++]; lst
b1=5; b2=8; 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 A029952 and A029803.

A259387 Palindromic numbers in bases 4 and 9 written in base 10.

Original entry on oeis.org

0, 1, 2, 3, 5, 10, 255, 273, 373, 546, 2550, 2730, 2910, 16319, 23205, 54215, 1181729, 1898445, 2576758, 3027758, 3080174, 4210945, 9971750, 163490790, 2299011170, 6852736153, 6899910553, 160142137430, 174913133450, 204283593150, 902465909895, 1014966912315, 2292918574418, 9295288254930, 11356994802010, 11372760382810, 38244097345762
Offset: 1

Views

Author

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

Keywords

Examples

			273 is in the sequence because 273_10 = 333_9 = 10101_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, 9]; If[palQ[pp, 4], AppendTo[lst, pp]; Print[pp]]; k++]; lst
b1=4; b2=9; 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 A029955.

A259388 Palindromic numbers in bases 5 and 9 written in base 10.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 109, 246, 282, 564, 701, 22386, 32152, 41667, 47653, 48553, 1142597, 1313858, 1412768, 1677684, 12607012902, 19671459008, 20134447808, 24208576998, 24863844904, 26358878059
Offset: 1

Views

Author

Robert G. Wilson v, Jul 16 2015

Keywords

Examples

			246 is in the sequence because 246_10 = 303_9 = 1441_5.

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, 9]; If[palQ[pp, 5], AppendTo[lst, pp]; Print[pp]]; k++]; lst
b1=5; b2=9; 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 A029952 and A029955.

A259389 Palindromic numbers in bases 6 and 9 written in base 10.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 7, 80, 154, 191, 209, 910, 3740, 5740, 8281, 16562, 16814, 2295481, 2300665, 2350165, 2439445, 2488945, 2494129, 2515513, 7971580, 48307924, 61281793, 69432517, 123427622, 124091822, 124443290, 55854298990, 184314116750, 185794441250, 187195815770, 327925630018, 7264479038060, 27832011695551
Offset: 1

Views

Author

Eric A. Schmidt and Robert G. Wilson v, Jul 17 2015

Keywords

Examples

			209 is in the sequence because 209_10 = 252_9 = 545_6.

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, 9]; If[palQ[pp, 6], AppendTo[lst, pp]; Print[pp]]; k++]; lst
b1=6; b2=9; lst={}; Do[d1=IntegerDigits[n, b1]; d2=IntegerDigits[n, b2]; If[d1==Reverse[d1]&&d2==Reverse[d2], AppendTo[lst, n]], {n, 0, 1000000}]; lst (* Vincenzo Librandi, Jul 17 2015 *)

Formula

Intersection of A029953 and A029955.

A056130 Palindromic primes in bases 2 and 4.

Original entry on oeis.org

3, 5, 17, 257, 5189, 65537, 83269, 86293, 1053953, 1066049, 1134929, 1311749, 1380629, 16864513, 17060929, 17909009, 18153809, 18171217, 21251141, 22103317, 289423441, 290455889, 290735441, 336662789, 336925957, 340873541
Offset: 1

Views

Author

Robert G. Wilson v, Jul 29 2000

Keywords

Comments

Intersection of A016041 and A029972.
Subsequence of primes of A097856. - Michel Marcus, Nov 07 2015

Examples

			5 is 101 (base 2) and 11 (base 4), that are both palindromic.

Links

Crossrefs

Cf. A016041 and A029972.

Programs

  • Mathematica
    Do[If[PrimeQ[n], t = RealDigits[n, 4][[1]]; If[FromDigits[t] == FromDigits[Reverse[t]], s = RealDigits[n, 2][[1]]; If[FromDigits[s] == FromDigits[Reverse[s]], Print[n]]]], {n, 1, 10^8, 2}]
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