%I #37 Sep 08 2022 08:45:14
%S 0,1,2,3,4,5,6,7,8,9,11,252,494,545,767,818,989,2882,4554,61416,94249,
%T 177771,256652,335533,1388831,4165614,8837388,31744713,102757201,
%U 103595301,123616321,124454421,207535702,208373802,212313212,229232922
%N Numbers palindromic in bases 10 and 17.
%H Robert G. Wilson v, <a href="/A097855/b097855.txt">Table of n, a(n) for n = 1..70</a> (first 67 terms from Ray Chandler)
%t 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, 17], AppendTo[l, a]], {n, 40000}]; l (* _Robert G. Wilson v_, Sep 03 2004 *)
%t b1=10; b2=17; 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 *)
%t Select[Range[0, 10^5],
%t PalindromeQ[#] && # == IntegerReverse[#, 17] &] (* _Robert Price_, Nov 09 2019 *)
%o (Magma) [n: n in [0..10000000] | Intseq(n, 10) eq Reverse(Intseq(n, 10))and Intseq(n, 17) eq Reverse(Intseq(n, 17))]; // _Vincenzo Librandi_, Nov 23 2014
%Y Cf. A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968, A029969, A029970, A029731, A099165.
%K base,nonn
%O 1,3
%A _Cino Hilliard_, Aug 31 2004
%E More terms from _Robert G. Wilson v_, Sep 03 2004
%E Term 0 prepended by _Robert G. Wilson v_, Oct 07 2014
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