A307802 Number of palindromic octagonal numbers of length n whose index is also palindromic.

3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1,1

Comments

Is there a nonzero term beyond a(1)?

Links

Table of n, a(n) for n=1..20.

P. De Geest, Palindromic Squares

Eric Weisstein's World of Mathematics, Palindromic Number

Example

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.

Mathematica

A057107 = {0, 1, 8, 8008, 120232021, 124060421, 161656161, 185464581, 544721127445, 616947749616, 3333169613333, 3333802083333, 6506939396056, 12212500521221, 5466543663456645, 3310988011108890133, 520752145595541257025, 336753352502205253357633, 5882480463134313640842885, 102573006711888117600375201, 8025741496504444056941475208, 18651903272292929227230915681, 33582545421505050512454528533};
A057106 = {0, 1, 2, 52, 6331, 6431, 7341, 7863, 426115, 453486, 1054067, 1054167, 1472746, 2017631, 42687015, 1050553507, 13175129925, 335038979077, 1400295262095, 5847307263801, 51722791547842, 78849864240621, 105802560494387};
Table[Length[Select[A057106[[Table[Select[Range[20], IntegerLength[A057107[[#]]] ==  n || (n == 1 && A057107[[#]] == 0) &], {n, 20}][[n]]]], PalindromeQ[#] &]], {n, 20}]

Crossrefs

Cf. A000567, A057107, A057106, A059870, A307790, A307791.

Sequence in context: A160540 A186718 A319625 * A169585 A045840 A181000

Adjacent sequences: A307799 A307800 A307801 * A307803 A307804 A307805

Keyword

nonn,base,hard,more

Author

Robert Price, Apr 29 2019

Status

approved