A270034 - OEIS

A270034

a(n) is the smallest b for which the base-b representation of n contains at least one 8 (or 0 if no such base exists).

0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 9, 10, 11, 12, 13, 14, 15, 16, 17, 9, 19, 10, 21, 11, 23, 12, 25, 13, 9, 14, 29, 10, 31, 16, 11, 17, 35, 9, 37, 19, 13, 10, 41, 14, 43, 11, 9, 23, 47, 12, 49, 10, 17, 13, 53, 9, 11, 14, 19, 29, 59, 10, 61, 31, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9

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OFFSET

1,8

COMMENTS

a(n) > 0 for n >= 17 since 18 is n written in base n-8.

The only perfect k-th powers (k >= 2) that can appear in this sequence are m^k with 2 <= m <= 8 and k a prime number.

LINKS

Nathan Fox, Table of n, a(n) for n = 1..10000

MATHEMATICA

Table[SelectFirst[Range[9, 1200], DigitCount[n, #, 8] > 0 &], {n, 17, 120}] (* Michael De Vlieger, Mar 10 2016, Version 10 *)

PROG

(PARI) b(n) = if ((n<17) && (n!=8), 0, my(b=9); while(!vecsearch(Set(digits(n, b)), 8), b++); b); \\ Michel Marcus, Mar 10 2016