A307832 Number of palindromic decagonal (10-gonal) numbers of length n whose index is also palindromic.

2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1,1

Comments

Is there a nonzero term beyond a(12)?

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 is only one palindromic decagonal number of length 3 whose index is also palindromic, 8->232. Thus, a(3)=1.

Mathematica

A307827 = {0, 1, 232, 27972, 76867, 25555552, 7154664517, 158229922851, 2028787878202, 2040061600402, 2733623263372, 52667666676625, 675972505279576, 28519896169891582, 73542836563824537, 74529570707592547, 25552469511596425552, 27835145788754153872, 62740719088091704726, 67047523077032574076, 77979812588521897977, 107838025535520838701};
A307829 = {0, 1, 8, 84, 139, 2528, 42293, 198891, 712178, 714154, 826684, 3628625, 12999736, 84439174, 135593913, 136500523, 2527472528, 2637951184, 3960451966, 4094127596, 4415308953, 5192254461};
Table[Length[ Select[A307829[[Table[ Select[Range[20], IntegerLength[A307827[[#]]] == n || (n == 1 && A307827[[#]] == 0) &], {n, 20}][[n]]]], PalindromeQ[#] &]], {n, 20}]

Crossrefs

Cf. A001107, A307827, A307829, A307830, A307831, A307808.

Sequence in context: A258822 A353373 A064530 * A037047 A118917 A325045

Adjacent sequences: A307829 A307830 A307831 * A307833 A307834 A307835

Keyword

nonn,base,hard,more

Author

Robert Price, Apr 30 2019

Status

approved