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 A270032 a(n) is the smallest b for which the base-b representation of n contains at least one 6 (or 0 if no such base exists). 9
 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 7, 8, 9, 10, 11, 12, 13, 7, 15, 8, 17, 9, 19, 10, 7, 11, 23, 8, 25, 13, 9, 7, 29, 10, 31, 8, 11, 17, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 7, 9, 9, 9, 9, 9, 9, 7, 10, 10, 10, 10, 10, 10, 7, 8, 11, 11, 11, 11, 11, 7, 12, 8, 12, 12, 12 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS a(n) > 0 for n >= 13 since 16 is n written in base n-6. The only perfect k-th powers (k >= 2) that can appear in this sequence are m^k with 2 <= m <= 6 and k a prime number. LINKS Nathan Fox, Table of n, a(n) for n = 1..10000 MATHEMATICA Table[SelectFirst[Range[7, 1200], DigitCount[n, #, 6] > 0 &], {n, 13, 120}] (* Michael De Vlieger, Mar 10 2016, Version 10 *) PROG (PARI) a(n) = if ((n<13) && (n!=6), 0, my(b=7); while(!vecsearch(Set(digits(n, b)), 6), b++); b); \\ Michel Marcus, Mar 10 2016 CROSSREFS Cf. A270027, A270028, A216194, A270029, A270030, A270031, A270033, A270034, A270035, A270042. Sequence in context: A182796 A079683 A115528 * A305671 A228633 A106226 Adjacent sequences:  A270029 A270030 A270031 * A270033 A270034 A270035 KEYWORD nonn,base AUTHOR Nathan Fox, Mar 08 2016 STATUS approved

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Last modified September 15 16:12 EDT 2019. Contains 327078 sequences. (Running on oeis4.)