A029969 Numbers that are palindromic in bases 10 and 14.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 323, 464, 717, 858, 999, 1111, 39593, 59095, 420024, 546645, 9046409, 9578759, 9813189, 535505535, 564303465, 595121595, 5736116375, 6758008576, 10476867401, 11652825611, 14203330241

Offset

1,3

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..70 (first 63 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, 14], AppendTo[l, a]], {n, 300000}]; l (* Robert G. Wilson v, Sep 03 2004 *)
b1=10; b2=14; 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, Nov 23 2014 *)
palQ[n_]:=Module[{idn14=IntegerDigits[n, 14]}, n==IntegerReverse[n]&&idn14==Reverse[idn14]]; Select[Range[10^7], palQ] (* The program uses the IntegerReverse function from Mathematica version 10 *) (* Harvey P. Dale, Apr 23 2016 *)
Select[Range[0, 10^5],
PalindromeQ[#] && # == IntegerReverse[#, 14] &] (* Robert Price, Nov 09 2019 *)

Prog

(Magma) [n: n in [0..10000000] | Intseq(n, 10) eq Reverse(Intseq(n, 10))and Intseq(n, 14) eq Reverse(Intseq(n, 14))]; // Vincenzo Librandi, Nov 23 2014

Crossrefs

Cf. A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968, A029970, A029731, A097855, A099165.

Sequence in context: A029968 A097855 A250408 * A029731 A248899 A029970

Adjacent sequences: A029966 A029967 A029968 * A029970 A029971 A029972

Keyword

nonn,base

Author

Patrick De Geest

Status

approved