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 A216194 a(n) = Smallest b for which the base b representation of n contains at least one 2 (or 0 if no such base exists). 14
 0, 3, 0, 0, 3, 3, 3, 3, 4, 4, 3, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 10, 3, 4, 11, 3, 3, 3, 3, 4, 4, 3, 4, 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, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 4, 3, 6, 5, 3, 3, 3, 3, 4, 4, 3, 6, 4, 3, 3, 3, 3, 3, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n)=3 if and only if n is in A074940. a(n) > 0 for n >= 5 since 12 is n written in base n-2. 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 849. The first n for which a(n)=8 is 1084. The first n for which a(n)=10 is 28. The second is 243. The first n for which a(n)=11 is 31. The second is 58130496. a(n)<=11 for all n with fewer than 3000 base 10 digits. No n for which a(n)>11 has been found. LINKS Nathan Fox, Table of n, a(n) for n = 1..10000 MAPLE firstNTerms:=proc(n) local b, i, rep, L: L:=[]: for i from 5 to n do b:=3: while true do rep:=convert(i, base, b): if evalb(2 in rep) then L:=[op(L), b]: break: fi: b:=b+1: od: od: L: end: MATHEMATICA sb2[n_]:=Module[{b=3}, While[DigitCount[n, b, 2]<1, b++]; b]; Array[sb2, 110, 5] (* Harvey P. Dale, Jan 16 2016 *) Table[SelectFirst[Range[3, 1200], DigitCount[n, #, 2] > 0 &], {n, 5, 120}] (* Michael De Vlieger, Mar 09 2016, Version 10 *) PROG (PARI) a(n) = if ((n<5) && (n!=2), 0, my(b=3); while (! vecsearch(vecsort(digits(n, b)), 2), b++); b); \\ Michel Marcus, Aug 06 2014, Mar 11 2016 CROSSREFS Cf. A216192, A270027, A270028, A270029, A270030, A270031, A270032, A270033, A270034, A270035. Sequence in context: A178153 A267794 A282499 * A365462 A279168 A111787 Adjacent sequences: A216191 A216192 A216193 * A216195 A216196 A216197 KEYWORD nonn,easy,base AUTHOR Nathan Fox, Mar 12 2013 EXTENSIONS Modified the definition to make the offset 1 by Nathan Fox, Mar 10 2016 STATUS approved

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Last modified April 25 09:56 EDT 2024. Contains 371967 sequences. (Running on oeis4.)