A065531 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,5

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

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 *)

CROSSREFS

Cf. A016038, A047811, A037183, A107129.

Essentially the same as A135551.

Sequence in context: A085693 A067995 A135551 * A366574 A256558 A239281

Adjacent sequences: A065528 A065529 A065530 * A065532 A065533 A065534

KEYWORD

easy,nonn,base

AUTHOR

Naohiro Nomoto, Dec 02 2001

STATUS

approved