Triangle of bases for which the least number is palindromic for n bases.

2, 2, 4, 3, 4, 9, 2, 4, 6, 20, 5, 8, 11, 17, 35, 9, 11, 14, 19, 29, 59, 3, 6, 9, 15, 19, 39, 79, 11, 14, 19, 23, 29, 39, 59, 119, 14, 17, 19, 29, 35, 44, 59, 89, 179, 7, 9, 21, 23, 32, 43, 65, 87, 131, 263, 5, 10, 17, 20, 27, 35, 41, 62, 83, 125, 251

1

See A037183 for the numbers, which can also be obtained by adding 1 to the last number in each row. Note that the plot appears to have upper and lower parts. The upper part consists of bases for which the palindrome has two digits.

T. D. Noe, Plot of 50 rows

T. D. Noe, Table of 50 rows

Eric W. Weisstein, MathWorld: Palindromic Number

(Mma) Table[Flatten[Position[Table[s = IntegerDigits[n, m]; s == Reverse[s], {m, 2, n - 1}], True] + 1], {n, {3, 5, 10, 21, 36, 60, 80, 120, 180, 264, 252, 360, 300, 960, 900, 720, 1080, 1440, 1800, 1680}}]

Cf. A037183, S000573, S000574.

nonn,base,tabl

T. D. Noe, Apr 13 2015