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A270030
a(n) is the smallest b for which the base-b representation of n contains at least one 4 (or 0 if no such base exists).
11
0, 0, 0, 5, 0, 0, 0, 0, 5, 6, 7, 8, 9, 5, 11, 6, 13, 7, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 5, 7, 7, 7, 7, 5, 8, 8, 8, 8, 5, 6, 9, 9, 9, 5, 5, 5, 5, 5, 5, 11, 11, 6, 7, 5, 12, 12, 12, 6, 5, 6, 6, 6, 6, 5, 6, 14, 7, 8, 5, 5, 5, 5, 5, 5, 16, 6, 7, 7, 5, 7, 7, 6, 7, 5, 9, 18, 18, 6, 5, 19
OFFSET
1,4
COMMENTS
a(n) > 0 for n >= 9 since 14 is n written in base n-4.
The only perfect k-th powers (k >= 2) that can appear in this sequence are 2^k, 3^k, or 4^k, with k a prime number.
MATHEMATICA
Table[SelectFirst[Range[5, 10^3], DigitCount[n, #, 4] > 0 &], {n, 9, 120}] (* Michael De Vlieger, Mar 10 2016, Version 10 *)
PROG
(PARI) a(n) = if ((n<9) && (n!=4), 0, my(b=5); while(!vecsearch(Set(digits(n, b)), 4), b++); b); \\ Michel Marcus, Mar 10 2016
KEYWORD
nonn,base
AUTHOR
Nathan Fox, Mar 08 2016
STATUS
approved