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

1,1

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A002113, A235922.

Sequence in context: A183736 A105238 A252396 * A097617 A160402 A243364

Adjacent sequences: A236363 A236364 A236365 * A236367 A236368 A236369

Keyword

nonn,base

Author

Vladimir Shevelev, Jan 23 2014

Extensions

Name clarified by Jon E. Schoenfield, Sep 21 2022

Status

approved