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%I #19 Nov 09 2019 10:40:07
%S 0,1,2,3,5,55,373,393,666,787,939,7997,53235,55255,55655,57675,506605,
%T 1801081,2215122,3826283,3866683,5051505,5226225,5259525,5297925,
%U 5614165,5679765,53822835,623010326,954656459,51717171715
%N Palindromic in bases 4 and 10.
%H Robert G. Wilson v, <a href="/A029961/b029961.txt">Table of n, a(n) for n = 1..56</a>
%H P. De Geest, <a href="http://www.worldofnumbers.com/nobase10.htm">Palindromic numbers beyond base 10</a>
%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, 4], AppendTo[l, a]], {n, 1000000}]; l (* _Robert G. Wilson v_, Sep 30 2004 *)
%t Select[Range[0, 10^5],
%t PalindromeQ[#] && # == IntegerReverse[#, 4] &] (* _Robert Price_, Nov 09 2019 *)
%Y Cf. A007632, A007633, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968, A029969, A029970, A029731, A097855, A099165.
%K nonn,base
%O 1,3
%A _Patrick De Geest_
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