Irregular array of positive palindromic square pyramidal numbers in bases 2 to 10.
1, 101, 1100110011, 110011000101101000110011, 1, 10101, 10202020201, 1, 11, 313, 22022, 30303, 123321, 212212, 1112111, 1, 12344321, 1, 5, 22, 131, 1441, 3443, 4441444, 1, 5, 555, 1525251, 1621164444611261, 1, 5, 1, 5, 33, 111, 122221, 123333321, 123444444321, 123455555554321, 123456666666654321, 123456777777777654321, 123456788888888887654321, 1, 5, 55, 1992991
1
See S000380 for the numbers that create these palindromic square pyramidal numbers. It appears that all these bases have only a finite number of terms.
T. D. Noe, Plot of 46 terms
Eric W. Weisstein, MathWorld: Square Pyramidal Numbers
(Mma) (* this is the base 2 case, where t2 comes from S000380 *) pyr[n_] := n*(n+1)*(2*n+1)/6; Table[FromDigits[IntegerDigits[pyr[n], 2]], {n, t2}]
Cf. S000376, S000377, S000380.
nonn,base,fini
T. D. Noe, Nov 24 2014