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A270034
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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).
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11
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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
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1,8
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COMMENTS
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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.
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LINKS
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MATHEMATICA
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Table[SelectFirst[Range[9, 1200], DigitCount[n, #, 8] > 0 &], {n, 17, 120}] (* Michael De Vlieger, Mar 10 2016, Version 10 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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