Irregular array of positive palindromic tetrahedral numbers in bases 2 to 9.
1, 10100101, 111000111, 101101101101, 1, 11, 101, 202, 2002, 111111, 202202, 112121211, 112222222211, 201000222000102, 1102111111112011, 1, 22, 3112112113, 1122123212211, 1, 4, 101101, 1, 4, 55, 2332, 1, 4, 1661, 6364334636, 1, 4, 707, 5555, 25477452, 1534114351
1
See S000376 for the numbers that create these palindromic tetrahedral numbers. It appears that only base 9 has an infinite number of terms. The last three terms for base 9 are conjectured. See S000378 and S000379.
T. D. Noe, Plot of 51 terms
T. D. Noe, Table of 51 terms
Eric W. Weisstein, MathWorld: Tetrahedral Number
(Mma) (* this is the base 2 case, where t2 comes from S000376 *) tet[n_] := n*(n + 1)*(n + 2)/6; Table[FromDigits[IntegerDigits[tet[n], 2]], {n, t2}]
Cf. A006029, A006030 (the base 10 terms), S000376, S000378, S000379.
nonn,base
T. D. Noe, Nov 21 2014