A029970 Numbers that are palindromic in bases 10 and 15.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 828, 858, 888, 919, 949, 979, 1551, 2772, 23632, 25552, 60106, 67576, 465564, 477774, 489984, 515515, 527725, 17577571, 26144162, 28300382, 39399393, 47999974, 69455496, 2118008112, 8050880508

Offset

1,3

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..72 (first 69 terms from Ray Chandler)

P. De Geest, Palindromic numbers beyond base 10

Mathematica

NextPalindrome[n_] := Block[{l = Floor[ Log[10, n] + 1], idn = IntegerDigits[n]}, If[ Union[idn] == {9}, Return[n + 2], If[l < 2, Return[n + 1], If[ FromDigits[ Reverse[ Take[idn, Ceiling[l/2]] ]] FromDigits[ Take[idn, -Ceiling[l/2]]], FromDigits[ Join[ Take[idn, Ceiling[l/2]], Reverse[ Take[idn, Floor[l/2]] ]]], idfhn = FromDigits[ Take[idn, Ceiling[l/2]]] + 1; idp = FromDigits[ Join[ IntegerDigits[idfhn], Drop[ Reverse[ IntegerDigits[idfhn]], Mod[l, 2]] ]]] ]]]; palQ[n_Integer, base_Integer] := Block[{idn = IntegerDigits[n, base]}, idn == Reverse[idn]]; l = {0}; a = 0; Do[a = NextPalindrome[a]; If[ palQ[a, 15], AppendTo[l, a]], {n, 200000}]; l (* Robert G. Wilson v, Sep 03 2004 *)
b1=10; b2=15; 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, Nov 23 2014 *)
Select[Range[0, 10^5], PalindromeQ[#] && # == IntegerReverse[#, 15] &] (* Robert Price, Nov 09 2019 *)

Prog

(Magma) [n: n in [0..10000000] | Intseq(n, 10) eq Reverse(Intseq(n, 10))and Intseq(n, 15) eq Reverse(Intseq(n, 15))]; // Vincenzo Librandi, Nov 23 2014

Crossrefs

Cf. A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968, A029969, A029731, A097855, A099165.

Sequence in context: A029969 A029731 A248899 * A143265 A109841 A174234

Adjacent sequences: A029967 A029968 A029969 * A029971 A029972 A029973

Keyword

nonn,base

Author

Patrick De Geest

Status

approved