A037183 Smallest number that is palindromic (with at least 2 digits) in n bases.

3, 5, 10, 21, 36, 60, 80, 120, 180, 264, 252, 360, 300, 960, 900, 720, 1080, 1440, 1800, 1680, 2160, 2880, 5616, 3780, 2520, 3600, 6120, 6720, 6300, 5040, 11340, 7560, 14112, 10800, 9240, 10080, 13860, 12600, 31200, 15120, 22680, 20160, 18480, 39312, 33264, 39600, 25200, 30240

Offset: 1

Author

Erich Friedman, Dec 11 1999

Keywords

• nonn
• base
• nice

Comments

Smallest number k that is palindromic in n bases b, 1 < b < k.

Only a(1), a(2), a(3), a(4) & a(7) are not congruent to 0 (mod 12). - Robert G. Wilson v, Oct 21 2014

First occurrence of k beginning with 0 in A135551. - Robert G. Wilson v, Jun 30 2017

Examples

			3 = 11 in base 2.
5 = 101 in base 2 and 11 in base 4.
10 is a palindrome in bases 3, 4 and 9: 101(3), 22(4) and 11(9). So a(3)=10.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..342 (first 100 terms from Giovanni Resta)
• Robert G. Wilson v, Smallest number which is palindromic in n bases or 0 if no such number is known

Crossrefs

Cf. A065531, A107129, A135549.

Programs

Mathematica

f[n_] := Module[{idn, s = Floor@ Sqrt[n + 1] - 1}, lng = Table[ If[ Reverse[ idn = IntegerDigits[n, b]] == idn, {b}, Sequence @@ {}], {b, 2, s + 1}]; If[ IntegerQ@ Sqrt[n + 1], -1, 0] + Length@ lng + Count[ Mod[n, Range@ s], 0]]; f[n_] := 0 /; n < 3; t = Table[0, {700}]; k = 3; While[k < 1100000001, a = f[k]; If[ t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++]; Take[t, 310] (* Robert G. Wilson v, Nov 02 2014 *)

Extensions

More terms from David W. Wilson