A050812 Number of times n is palindromic in bases b, 2 <= b <= 10.

9, 9, 8, 8, 7, 7, 5, 5, 4, 3, 3, 1, 1, 1, 1, 2, 2, 2, 2, 0, 2, 3, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 0, 3, 1, 1, 1, 1, 2, 2, 0, 1, 1, 2, 2, 2, 0, 1, 3, 1, 2, 0, 1, 1, 1, 1, 3, 1, 3, 1, 2, 1, 0, 1, 1, 1, 2, 1, 0, 0, 1, 2, 0, 3, 1, 2, 1, 0, 3

Offset: 0

Author

Patrick De Geest, Oct 15 1999

Keywords

• nonn
• base

Examples

			a(121) = 4 since 121_10, 171_8, 232_7 and 11111_3 are palindromes.
		

Links

• T. D. Noe, Table of n, a(n) for n = 0..10000
• Patrick De Geest, Palindromic numbers beyond base 10

Crossrefs

Cf. A050813, A016038, A002113.

Programs

Mathematica

Table[Count[Table[IntegerDigits[n,b],{b,2,10}],?(#==Reverse[#]&)],{n,0,90}] (* _Harvey P. Dale, Aug 18 2012 *)

PARI

a(n) = sum(b=2, 10, my(d=digits(n, b)); d == Vecrev(d)); \\ Michel Marcus, Sep 09 2021

Python

from sympy.ntheory.digits import digits
def ispal(n, b):
    digs = digits(n, b)[1:]
    return digs == digs[::-1]
def a(n): return sum(ispal(n, b) for b in range(2, 11))
print([a(n) for n in range(87)]) # Michael S. Branicky, Sep 09 2021