A236366 a(n) is the concatenation of the numbers k, 2 <= k <= 9, such that the base-k representation of n is a palindrome; a(n) = 0 if there is no such base.

23456789, 3456789, 2456789, 356789, 246789, 5789, 2689, 379, 28, 349, 0, 5, 3, 6, 24, 37, 24, 58, 0, 39, 246, 0, 3, 57, 4, 35, 28, 36, 4, 9, 25, 7, 2, 4, 6, 58, 6, 4, 0, 379, 5, 4, 6, 0, 28, 45, 0, 7, 6, 79, 24, 35, 0, 8, 46, 3, 57, 0, 4, 9, 6, 5, 248, 7, 248

Offset: 1

Author

Vladimir Shevelev, Jan 23 2014

Keywords

• nonn
• base

Examples

			Let n = 29. In bases 2, 3, ..., 9 the representations of 29 are 11101_2, 1002_3, 131_4, 104_5, 45_6, 41_7, 35_8, 32_9. In this list only 131_4 is a palindrome, so a(29) = 4.
		

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A002113, A235922.

Programs

Mathematica

Table[FromDigits[1+Flatten[Position[Map[Reverse[#]==#&,Map[IntegerDigits[n,#]&,Range[2,9]]],True]]],{n,50}]

Python

from sympy.ntheory import digits
def c(n, b): d = digits(n, b)[1:]; return d == d[::-1]
def a(n): return int("0"+"".join(d for d in "23456789" if c(n, int(d))))
print([a(n) for n in range(1, 66)]) # Michael S. Branicky, Sep 21 2022

Extensions

Name clarified by Jon E. Schoenfield, Sep 21 2022