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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 6 20:15 EST 2023. Contains 360111 sequences. (Running on oeis4.)