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 A270028 a(n) is the smallest b >= 3 for which the base-b representation of n contains at least one 1 (or 0 if no such base exists). 11
 3, 0, 3, 3, 3, 4, 3, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 5, 3, 3, 3, 6, 3, 6, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If we drop the b >= 3 requirement, then this sequence becomes A007395 (the constant 2 sequence). a(n) > 0 for n >= 3 since the base-(n-1) representation of n is 11. a(n)=3 if and only if n is in A081606. The only perfect k-th powers (k >= 2) that can appear in this sequence are 2^k with k a prime number. The first n for which a(n)=7 is 560. The first n for which a(n)=8 is 870899850. The first n for which a(n)=10 is 871017138. The first n for which a(n)=11 is 65473886952. The first n for which a(n)=12 is 65473886954. LINKS Nathan Fox, Table of n, a(n) for n = 1..10000 MATHEMATICA Table[SelectFirst[Range[3, 10], DigitCount[n, #, 1] > 0 &], {n, 3, 120}] (* Michael De Vlieger, Mar 10 2016, Version 10 *) PROG (PARI) a(n) = if (n==2, 0, my(b=3); while(!vecsearch(Set(digits(n, b)), 1), b++); b); \\ Michel Marcus, Mar 10 2016 CROSSREFS Cf. A270027, A216194, A270029, A270030, A270031, A270033, A270034, A270035, A270038. Sequence in context: A357062 A066851 A288571 * A167223 A341480 A261922 Adjacent sequences: A270025 A270026 A270027 * A270029 A270030 A270031 KEYWORD nonn,base AUTHOR Nathan Fox, Mar 08 2016 STATUS approved

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Last modified April 23 20:33 EDT 2024. Contains 371916 sequences. (Running on oeis4.)