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%I #8 Aug 11 2024 14:41:35
%S 3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N Number of palindromic octagonal numbers of length n whose index is also palindromic.
%C Is there a nonzero term beyond a(1)?
%H P. De Geest, <a href="https://www.worldofnumbers.com/square.htm">Palindromic Squares</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PalindromicNumber.html">Palindromic Number</a>
%e There are only three palindromic octagonal numbers of length 1 whose index is also palindromic, 0->0, 1->1, and 2->8. Thus, a(1)=3.
%t A057107 = {0, 1, 8, 8008, 120232021, 124060421, 161656161, 185464581, 544721127445, 616947749616, 3333169613333, 3333802083333, 6506939396056, 12212500521221, 5466543663456645, 3310988011108890133, 520752145595541257025, 336753352502205253357633, 5882480463134313640842885, 102573006711888117600375201, 8025741496504444056941475208, 18651903272292929227230915681, 33582545421505050512454528533};
%t A057106 = {0, 1, 2, 52, 6331, 6431, 7341, 7863, 426115, 453486, 1054067, 1054167, 1472746, 2017631, 42687015, 1050553507, 13175129925, 335038979077, 1400295262095, 5847307263801, 51722791547842, 78849864240621, 105802560494387};
%t Table[Length[Select[A057106[[Table[Select[Range[20], IntegerLength[A057107[[#]]] == n || (n == 1 && A057107[[#]] == 0) &], {n, 20}][[n]]]], PalindromeQ[#] &]], {n, 20}]
%Y Cf. A000567, A057107, A057106, A059870, A307790, A307791.
%K nonn,base,hard,more
%O 1,1
%A _Robert Price_, Apr 29 2019