A029965 Palindromic in bases 9 and 10.

0, 1, 2, 3, 4, 5, 6, 7, 8, 191, 282, 373, 464, 555, 646, 656, 6886, 25752, 27472, 42324, 50605, 626626, 1540451, 1713171, 1721271, 1828281, 1877781, 1885881, 2401042, 2434342, 2442442, 2450542, 3106013, 3114113, 3122213, 3163613

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base

Links

• Robert G. Wilson v and Ray Chandler, Table of n, a(n) for n = 1..66 (terms < 10^18, first 52 terms from Robert G. Wilson v)
• P. De Geest, Palindromic numbers beyond base 10

Crossrefs

Cf. A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029966, A029967, A029968, A029969, A029970, A029731, A097855, A099165.

Programs

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, 9], AppendTo[l, a]], {n, 10000}]; l (* Robert G. Wilson v, Sep 30 2004 *)
pQ[n_,k_]:=Reverse[x=IntegerDigits[n,k]]==x; t={}; Do[If[pQ[n,10] && pQ[n,9],AppendTo[t,n]],{n,3.2*10^6}]; t (* Jayanta Basu, May 25 2013 *)
Select[Range[0, 10^5],
PalindromeQ[#] && # == IntegerReverse[#, 9] &] (* Robert Price, Nov 09 2019 *)