A065531 Number of palindromes in all base b representations for n, for 2<=b<=n.

1, 0, 1, 1, 2, 1, 2, 2, 2, 3, 1, 2, 2, 2, 3, 3, 3, 3, 1, 3, 4, 2, 2, 4, 2, 4, 3, 4, 2, 3, 3, 3, 3, 3, 2, 5, 2, 3, 2, 5, 2, 4, 2, 3, 4, 4, 1, 5, 2, 4, 4, 5, 1, 4, 4, 4, 4, 2, 2, 6, 2, 3, 5, 4, 5, 4, 3, 4, 2, 4, 2, 6, 3, 3, 3, 3, 2, 6, 1, 7, 3, 4, 2, 6, 5, 3, 2, 5, 2, 5, 4, 5, 4, 2, 2, 6, 2, 5, 4, 7, 2, 4, 1, 6, 6

Offset: 1

Author

Naohiro Nomoto, Dec 02 2001

Keywords

• easy
• nonn
• base

Comments

a(1) = 1 by convention, which makes this sequence different from A135551.

Index of first occurrence of k in A037183. - Robert G. Wilson v, Oct 27 2014

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A016038, A047811, A037183, A107129.

Essentially the same as A135551.

Programs

Mathematica

f = Compile[{{n, Integer}}, Module[{b = 2, c = Floor@ If[ IntegerQ@ Sqrt[n + 1], -1, 0], idn, s = Floor@ Sqrt[n + 1] - 1}, c = c + Count[ Mod[n, Range@ s], 0]; s = s + 2; While[b < s, If[ Reverse[idn = IntegerDigits[n, b]] == idn, c++]; b++]; c]]; f[1] = 1; Array[f, 105] (* _Robert G. Wilson v, May 05 2025 *)