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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
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
Sequence in context: A331979 A005872 A035322 * A284105 A331928 A228632
KEYWORD
nonn,base
AUTHOR
Nathan Fox, Mar 08 2016
STATUS
approved

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Last modified April 25 09:49 EDT 2024. Contains 371967 sequences. (Running on oeis4.)