A135550 Number of bases b, 1 < b < n-1, in which n is a palindrome, allowing leading zeros when testing if a number is a palindrome.

0, 0, 0, 0, 1, 1, 2, 1, 3, 2, 4, 0, 5, 1, 3, 3, 5, 2, 6, 0, 6, 4, 2, 1, 8, 2, 4, 4, 6, 1, 8, 2, 6, 3, 4, 2, 10, 1, 3, 3, 9, 1, 8, 1, 4, 5, 4, 0, 11, 2, 6, 4, 6, 0, 8, 4, 8, 4, 2, 1, 14, 1, 4, 6, 8, 5, 7, 2, 7, 3, 6, 1, 14, 2, 3, 5, 4, 2, 9, 0, 12, 5, 4, 1, 14, 5, 3, 2, 7, 1, 13, 4, 6, 4, 2, 2

Offset: 0

Author

John P. Linderman, Feb 26 2008, Feb 28 2008

Keywords

• nonn
• base

Comments

Every integer n is a palindrome when expressed in unary, or in base n-1 (where it will be 11). So here we assume 1 < b < n-1.

Here 4 = 100 counts as a palindrome in base 2, since 00100 is palindromic.

Links

• Paul Tek, Table of n, a(n) for n = 0..10000
• John P. Linderman, Description of A135549-A135551 and A016038
• John P. Linderman, Perl program [Use the command: LEADING0S=1 palin.pl]

Crossrefs

Cf. A135549, A135551, A016038.