A307791 Number of palindromic heptagonal numbers of length n whose index is also palindromic.

3, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Robert Price, Apr 28 2019

Keywords

• nonn
• base
• hard
• more

Comments

Is there a nonzero term beyond a(4)?

Examples

			There is only one palindromic heptagonal number of length 4 whose index is also palindromic, 44->4774. Thus, a(4)=1.
		

Links

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

Crossrefs

Cf. A000566, A054910, A054971, A059869, A307765, A307766.

Programs

Mathematica

A054910 = {0, 1, 7, 55, 616, 3553, 4774, 60606, 848848, 4615164, 5400045, 6050506, 7165445617, 62786368726, 65331413356, 73665056637, 91120102119, 345546645543, 365139931563, 947927729749, 3646334336463, 7111015101117, 717685292586717, 19480809790808491, 615857222222758516, 1465393008003935641, 8282802468642082828, 15599378333387399551, 20316023422432061302};
A054971 = {0, 1, 2, 5, 16, 38, 44, 156, 583, 1359, 1470, 1556, 53537, 158476, 161656, 171657, 190914, 371778, 382173, 615769, 1207698, 1686537, 16943262, 88274141, 496329416, 765609041, 1820198063, 2497949426, 2850685772}; Table[Length[Select[A054971[[Table[Select[Range[19], IntegerLength[A054910[[#]]] ==  n || (n == 1 && A054910[[#]] == 0) &], {n, 19}][[n]]]], PalindromeQ[#] &]], {n, 19}]