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 A270029 a(n) is the smallest b for which the base-b representation of n contains at least one 3 (or 0 if no such base exists). 11
 0, 0, 4, 0, 0, 0, 4, 5, 6, 7, 4, 4, 4, 4, 4, 5, 5, 5, 4, 6, 6, 6, 4, 7, 7, 7, 4, 4, 4, 4, 4, 9, 5, 9, 4, 10, 10, 5, 4, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 17, 5, 5, 4, 5, 5, 7, 4, 7, 5, 7, 4, 4, 4, 4, 4, 5, 5, 5, 4, 5, 5, 5, 4, 5, 5, 5, 4, 4, 4, 4, 4, 5, 5, 5, 4, 26 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(n) > 0 for n >= 7 since 13 is n written in base n-3. The only perfect k-th powers (k >= 2) that can appear in this sequence are 2^k and 3^k with k a prime number. LINKS Nathan Fox, Table of n, a(n) for n = 1..10000 MATHEMATICA Table[SelectFirst[Range[4, 10^3], DigitCount[n, #, 3] > 0 &], {n, 7, 120}] (* Michael De Vlieger, Mar 10 2016, Version 10 *) PROG (PARI) a(n) = if ((n<7) && (n!=3), 0, my(b=4); while(!vecsearch(Set(digits(n, b)), 3), b++); b); \\ Michel Marcus, Mar 10 2016 CROSSREFS Cf. A270027, A270028, A216194, A270030, A270031, A270032, A270033, A270034, A270035, A270039. Sequence in context: A255263 A153011 A173532 * A028598 A272618 A265397 Adjacent sequences: A270026 A270027 A270028 * A270030 A270031 A270032 KEYWORD nonn,base AUTHOR Nathan Fox, Mar 08 2016 STATUS approved

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Last modified April 23 20:27 EDT 2024. Contains 371916 sequences. (Running on oeis4.)