Irregular array of positive numbers that form palindromic square pyramidal numbers in bases 2 to 10.
1, 2, 13, 342, 1, 6, 60, 1, 2, 5, 12, 13, 17, 19, 25, 1, 71, 1, 2, 3, 5, 10, 13, 87, 1, 2, 9, 85, 30031, 1, 2, 1, 2, 4, 6, 60, 546, 4920, 44286, 398580, 3587226, 32285040, 1, 2, 5, 181
1
Each row appears to be finite. See S000381 for the palindromic numbers formed by these numbers.
T. D. Noe, Plot of 46 terms
Eric W. Weisstein, MathWorld: Square Pyramidal Numbers
(Mma) ff[base_] := Module[{time0 = TimeUsed[], n = 0, t = {}, pyr, d}, While[TimeUsed[] - time0 < 300 && Length[t] < 100, n++; pyr = n*(n+1)*(2*n+1)/6; d = IntegerDigits[pyr, base]; If[d == Reverse[d], AppendTo[t, n]]]; t]; {t2, t3, t4, t5, t6, t7, t8, t9, t10} = ParallelMap[ff, Range[2, 10]]; Flatten[Join[{t2, t3, t4, t5, t6, t7, t8, t9, t10}]]
Cf. A000330 (square pyramidal numbers), S000381.
nonn,base,fini
T. D. Noe, Nov 24 2014