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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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.

A118595 Palindromes in base 4 (written in base 4).

Original entry on oeis.org

0, 1, 2, 3, 11, 22, 33, 101, 111, 121, 131, 202, 212, 222, 232, 303, 313, 323, 333, 1001, 1111, 1221, 1331, 2002, 2112, 2222, 2332, 3003, 3113, 3223, 3333, 10001, 10101, 10201, 10301, 11011, 11111, 11211, 11311, 12021, 12121, 12221, 12321, 13031
Offset: 1

Views

Author

Martin Renner, May 08 2006

Keywords

Comments

2*a(n) and 3*a(n) give palindromes in base 10 for any n. - Arkadiusz Wesolowski, Jun 22 2012
Equivalently, palindromes k (written in base 10) such that 3*k is a palindrome. - Bruno Berselli, Sep 12 2018

Crossrefs

Cf. A014192, A057148, A118594, A118595, A118596, A118597, A118598, A118599, A118600, A002113.

Programs

  • Mathematica
    (* get NextPalindrome from A029965 *) Select[NestList[NextPalindrome, 0, 290], Max@IntegerDigits@# < 4 &] (* Robert G. Wilson v, May 09 2006 *)
  • Python
    from gmpy2 import digits
def A118595(n):
    if n == 1: return 0
    y = (x:=1<<(n.bit_length()-2&-2))<<2
    return int((s:=digits(n-x,4))+s[-2::-1] if nChai Wah Wu, Jun 14 2024

Extensions

More terms from Robert G. Wilson v, May 09 2006

A118597 Palindromes in base 6 (written in base 6).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 11, 22, 33, 44, 55, 101, 111, 121, 131, 141, 151, 202, 212, 222, 232, 242, 252, 303, 313, 323, 333, 343, 353, 404, 414, 424, 434, 444, 454, 505, 515, 525, 535, 545, 555, 1001, 1111, 1221, 1331, 1441, 1551, 2002, 2112, 2222, 2332, 2442, 2552
Offset: 1

Views

Author

Martin Renner, May 08 2006

Keywords

Comments

Also palindromes with no digit greater than 5. - Harvey P. Dale, Nov 26 2019

Links

Crossrefs

Cf. A029953, A057148, A118594, A118595, A118596, A118597, A118598, A118599, A118600, A002113.

Programs

  • Mathematica
    (* get NextPalindrome from A029965 *) Select[NestList[NextPalindrome, 0, 125], Max@IntegerDigits@# < 6 &] (* Robert G. Wilson v, May 09 2006 *)
Select[FromDigits/@Tuples[Range[0,5],4],PalindromeQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 26 2019 *)
  • Python
    from sympy import integer_log
from gmpy2 import digits
def A118597(n):
    if n == 1: return 0
    y = 6*(x:=6**integer_log(n>>1,6)[0])
    return int((s:=digits(n-x,6))+s[-2::-1] if nChai Wah Wu, Jun 14 2024

Extensions

Corrected and extended by Robert G. Wilson v, May 09 2006

A118598 Palindromes in base 7 (written in base 7).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 11, 22, 33, 44, 55, 66, 101, 111, 121, 131, 141, 151, 161, 202, 212, 222, 232, 242, 252, 262, 303, 313, 323, 333, 343, 353, 363, 404, 414, 424, 434, 444, 454, 464, 505, 515, 525, 535, 545, 555, 565, 606, 616, 626, 636, 646, 656, 666, 1001
Offset: 1

Views

Author

Martin Renner, May 08 2006

Keywords

Crossrefs

Cf. A029954, A057148, A118594, A118595, A118596, A118597, A118598, A118599, A118600, A002113.

Programs

  • Mathematica
    (* get NextPalindrome from A029965 *) Select[NestList[NextPalindrome, 0, 109], Max@IntegerDigits@# < 7 &] (* Robert G. Wilson v, May 09 2006 *)
  • Python
    from sympy import integer_log
from gmpy2 import digits
def A118598(n):
    if n == 1: return 0
    y = 7*(x:=7**integer_log(n>>1,7)[0])
    return int((s:=digits(n-x,7))+s[-2::-1] if nChai Wah Wu, Jun 14 2024

Extensions

Corrected and extended by Robert G. Wilson v, May 09 2006

A118596 Palindromes in base 5 (written in base 5).

Original entry on oeis.org

0, 1, 2, 3, 4, 11, 22, 33, 44, 101, 111, 121, 131, 141, 202, 212, 222, 232, 242, 303, 313, 323, 333, 343, 404, 414, 424, 434, 444, 1001, 1111, 1221, 1331, 1441, 2002, 2112, 2222, 2332, 2442, 3003, 3113, 3223, 3333, 3443, 4004, 4114, 4224, 4334, 4444, 10001
Offset: 1

Views

Author

Martin Renner, May 08 2006

Keywords

Comments

Equivalently, palindromes k (written in base 10) such that 2*k is a palindrome. - Bruno Berselli, Sep 12 2018

Crossrefs

Cf. A029952, A057148, A118594, A118595, A118596, A118597, A118598, A118599, A118600, A002113.

Programs

  • Mathematica
    (* get NextPalindrome from A029965 *) Select[NestList[NextPalindrome, 0, 198], Max@IntegerDigits@# < 5 &] (* Robert G. Wilson v, May 09 2006 *)
Select[FromDigits/@IntegerDigits[Range[1000],5],PalindromeQ] (* Fred Patrick Doty, Aug 12 2017 *)
  • PARI
    is(n)=if(n<5, return(n>=0)); my(d=digits(n)); vecmax(d)<5 && Vecrev(d)==d \\ Charles R Greathouse IV, Aug 22 2017
  • Python
    from sympy import integer_log
from gmpy2 import digits
def A118596(n):
    if n == 1: return 0
    y = 5*(x:=5**integer_log(n>>1,5)[0])
    return int((s:=digits(n-x,5))+s[-2::-1] if nChai Wah Wu, Jun 14 2024

Extensions

More terms from Robert G. Wilson v, May 09 2006

A118599 Palindromes in base 8 (written in base 8).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 11, 22, 33, 44, 55, 66, 77, 101, 111, 121, 131, 141, 151, 161, 171, 202, 212, 222, 232, 242, 252, 262, 272, 303, 313, 323, 333, 343, 353, 363, 373, 404, 414, 424, 434, 444, 454, 464, 474, 505, 515, 525, 535, 545, 555, 565, 575, 606, 616
Offset: 1

Views

Author

Martin Renner, May 08 2006

Keywords

Crossrefs

Cf. A029803, A057148, A118594, A118595, A118596, A118597, A118598, A118599, A118600, A002113.

Programs

  • Mathematica
    (* get NextPalindrome from A029965 *) Select[NestList[NextPalindrome, 0, 70], Max@IntegerDigits@# < 8 &] (* Robert G. Wilson v, May 09 2006 *)
  • Python
    def A118599(n):
    if n == 1: return 0
    y = (x:=1<<(m:=n.bit_length()-2)-m%3)<<3
    return int((s:=oct(n-x)[2:])+s[-2::-1] if nChai Wah Wu, Jun 14 2024

Extensions

More terms from Robert G. Wilson v, May 09 2006

A118600 Palindromes in base 9 (written in base 9).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 11, 22, 33, 44, 55, 66, 77, 88, 101, 111, 121, 131, 141, 151, 161, 171, 181, 202, 212, 222, 232, 242, 252, 262, 272, 282, 303, 313, 323, 333, 343, 353, 363, 373, 383, 404, 414, 424, 434, 444, 454, 464, 474, 484, 505, 515, 525, 535, 545
Offset: 1

Views

Author

Martin Renner, May 08 2006

Keywords

Links

Crossrefs

Cf. A029955, A057148, A118594, A118595, A118596, A118597, A118598, A118599, A118600, A002113.

Programs

  • Mathematica
    (* get NextPalindrome from A029965 *) Select[NestList[NextPalindrome, 0, 62], Max@IntegerDigits@# < 9 &] (* Robert G. Wilson v, May 09 2006 *)
  • Python
    from gmpy2 import digits
def palgenbase(l,b): # generator of palindromes in base b <=10 of length <= 2*l, written in base b
    if l > 0:
        yield 0
        for x in range(1,l+1):
            for y in range(b**(x-1),b**x):
                s = digits(y,b)
                yield int(s+s[-2::-1])
            for y in range(b**(x-1),b**x):
                s = digits(y,b)
                yield int(s+s[::-1])
A118600_list = list(palgenbase(3,9)) # Chai Wah Wu, Dec 01 2014
  • Python
    from sympy import integer_log
from gmpy2 import digits
def A118600(n):
    if n == 1: return 0
    y = 9*(x:=9**integer_log(n>>1,9)[0])
    return int((s:=digits(n-x,9))+s[-2::-1] if nChai Wah Wu, Jun 14 2024

Extensions

More terms from Robert G. Wilson v, May 09 2006
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