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A270031 a(n) is the smallest b for which the base-b representation of n contains at least one 5 (or 0 if no such base exists). 11
0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 6, 7, 8, 9, 10, 11, 6, 13, 7, 15, 8, 17, 6, 19, 10, 7, 11, 23, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 6, 8, 8, 8, 8, 8, 6, 9, 9, 9, 9, 9, 6, 7, 10, 10, 10, 10, 6, 11, 7, 11, 11, 11, 6, 6, 6, 6, 6, 6, 6, 13, 13, 13, 7, 13, 6, 14, 14, 14, 14, 7, 6, 7, 7, 7, 7, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

a(n) > 0 for n >= 11 since 15 is n written in base n-5.

The only perfect k-th powers (k >= 2) that can appear in this sequence are m^k with 2 <= m <= 5 and k a prime number.

LINKS

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

MATHEMATICA

Table[SelectFirst[Range[6, 10^3], DigitCount[n, #, 5] > 0 &], {n, 11, 120}] (* Michael De Vlieger, Mar 10 2016, Version 10 *)

PROG

(PARI) a(n) = if ((n<11) && (n!=5), 0, my(b=6); while(!vecsearch(Set(digits(n, b)), 5), b++); b); \\ Michel Marcus, Mar 10 2016

CROSSREFS

Cf. A270027, A270028, A216194, A270029, A270030, A270032, A270033, A270034, A270035, A270041.

Sequence in context: A294887 A005872 A035322 * A284105 A228632 A229657

Adjacent sequences:  A270028 A270029 A270030 * A270032 A270033 A270034

KEYWORD

nonn,base

AUTHOR

Nathan Fox, Mar 08 2016

STATUS

approved

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Last modified July 15 16:09 EDT 2019. Contains 325049 sequences. (Running on oeis4.)