A307790 -id:A307790 - cp's OEIS frontend

A307801 Number of palindromic octagonal numbers with exactly n digits.

3, 0, 0, 1, 0, 0, 0, 0, 4, 0, 0, 2, 3, 1, 0, 1, 0, 0, 1, 0

Offset: 1

Robert Price, Apr 29 2019

Number of terms in A057107 with exactly n digits.

			There is only one 4 digit octagonal number that is palindromic, 8008.  Thus, a(4)=1.

G. J. Simmons, Palindromic powers, J. Rec. Math., 3 (No. 2, 1970), 93-98. [Annotated scanned copy] See page 95.

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

A057107 = {0, 1, 8, 8008, 120232021, 124060421, 161656161, 185464581, 544721127445, 616947749616, 3333169613333, 3333802083333, 6506939396056, 12212500521221, 5466543663456645, 3310988011108890133, 520752145595541257025, 336753352502205253357633, 5882480463134313640842885, 102573006711888117600375201, 8025741496504444056941475208, 18651903272292929227230915681, 33582545421505050512454528533}; Table[Length[Select[A054910, IntegerLength[#] == n || (n == 1 && # == 0) &]], {n, 20}] (* Robert Price, Apr 29 2019 *)

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

Original entry on oeis.org

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

Offset: 1

Robert Price, Apr 29 2019

Is there a nonzero term beyond a(1)?

			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.

Patrick De Geest, Palindromic Squares in bases 2 to 17
Eric Weisstein's World of Mathematics, Palindromic Number

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

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}]

cp's OEIS Frontend

A307801 Number of palindromic octagonal numbers with exactly n digits.

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