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

Author

Patrick De Geest

Keywords

• nonn
• base

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

Crossrefs

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

Programs

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

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 *)