A056641 Least positive integer k for which (b+1)^k is not palindromic in base b, b = 2, 3, 4, ...

4, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9

Offset: 2

Author

Helge Robitzsch (hrobi(AT)math.uni-goettingen.de), Aug 11 2000

Keywords

• nonn
• base

Comments

Sequence of run lengths is C(n,[ (n-1)/2 ]) (= A037952), n=1,2,3,...; sequence of b where a(b) != a(b-1), b >= 3, is C(b-1,[ (b-1)/2 ]) (= A001405).

Examples

			The 4th term is 4 because base 5 representations of (5+1)^1 = 11, (5+1)^2 = 121, (5+1)^3 = 1331, are all palindromic, while (5+1)^4 = 20141 is not.
		

Crossrefs

Cf. A037952, A001405, A305233.

Programs

Mathematica

palq[x_] := x == Reverse[x] Table[x = 0; While[palq[IntegerDigits[(t + 1)^x, t]], ++x]; x, {t, START, FINISH}] (* Dylan Hamilton, Aug 15 2010 *)