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 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). 11
 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 (list; graph; refs; listen; history; text; internal format)
 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 CROSSREFS Cf. A270027, A270028, A216194, A270029, A270030, A270031, A270032, A270033, A270035, A270044. Sequence in context: A226121 A337127 A193581 * A228635 A229660 A306757 Adjacent sequences: A270031 A270032 A270033 * A270035 A270036 A270037 KEYWORD nonn,base AUTHOR Nathan Fox, Mar 08 2016 STATUS approved

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Last modified February 28 19:33 EST 2024. Contains 370400 sequences. (Running on oeis4.)