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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

%I

%S 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,

%T 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,

%U 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

%N a(n) = Smallest b for which the base b representation of n contains at least one 2 (or 0 if no such base exists).

%C a(n)=3 if and only if n is in A074940.

%C a(n) > 0 for n >= 5 since 12 is n written in base n-2.

%C The only perfect k-th powers (k>=2) that can appear in this sequence are 2^k with k a prime number.

%C The first n for which a(n)=7 is 849.

%C The first n for which a(n)=8 is 1084.

%C The first n for which a(n)=10 is 28. The second is 243.

%C The first n for which a(n)=11 is 31. The second is 58130496.

%C a(n)<=11 for all n with fewer than 3000 base 10 digits. No n for which a(n)>11 has been found.

%H Nathan Fox, <a href="/A216194/b216194.txt">Table of n, a(n) for n = 1..10000</a>

%p firstNTerms:=proc(n) local b,i,rep,L:

%p L:=[]:

%p for i from 5 to n do

%p b:=3:

%p while true do

%p rep:=convert(i, base, b):

%p if evalb(2 in rep) then

%p L:=[op(L), b]:

%p break:

%p fi:

%p b:=b+1:

%p od:

%p od:

%p L:

%p end:

%t sb2[n_]:=Module[{b=3},While[DigitCount[n,b,2]<1,b++];b]; Array[sb2,110,5] (* _Harvey P. Dale_, Jan 16 2016 *)

%t Table[SelectFirst[Range[3, 1200], DigitCount[n, #, 2] > 0 &], {n, 5, 120}] (* _Michael De Vlieger_, Mar 09 2016, Version 10 *)

%o (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

%Y Cf. A216192, A270027, A270028, A270029, A270030, A270031, A270032, A270033, A270034, A270035.

%K nonn,easy,base

%O 1,2

%A _Nathan Fox_, Mar 12 2013

%E Modified the definition to make the offset 1 by _Nathan Fox_, Mar 10 2016

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Last modified October 18 14:48 EDT 2019. Contains 328161 sequences. (Running on oeis4.)