A236366 - OEIS

%I #16 Sep 22 2022 01:40:23

%S 23456789,3456789,2456789,356789,246789,5789,2689,379,28,349,0,5,3,6,

%T 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,

%U 4,6,0,28,45,0,7,6,79,24,35,0,8,46,3,57,0,4,9,6,5,248,7,248

%N 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.

%H Peter J. C. Moses, <a href="/A236366/b236366.txt">Table of n, a(n) for n = 1..5000</a>

%e 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.

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

%o (Python)

%o from sympy.ntheory import digits

%o def c(n, b): d = digits(n, b)[1:]; return d == d[::-1]

%o def a(n): return int("0"+"".join(d for d in "23456789" if c(n, int(d))))

%o print([a(n) for n in range(1, 66)]) # _Michael S. Branicky_, Sep 21 2022

%Y Cf. A002113, A235922.

%K nonn,base

%O 1,1

%A _Vladimir Shevelev_, Jan 23 2014

%E Name clarified by _Jon E. Schoenfield_, Sep 21 2022