cp's OEIS Frontend

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).

%I A216194 #35 Mar 11 2016 06:10:28
%S A216194 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 A216194 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 A216194 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 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).
%C A216194 a(n)=3 if and only if n is in A074940.
%C A216194 a(n) > 0 for n >= 5 since 12 is n written in base n-2.
%C A216194 The only perfect k-th powers (k>=2) that can appear in this sequence are 2^k with k a prime number.
%C A216194 The first n for which a(n)=7 is 849.
%C A216194 The first n for which a(n)=8 is 1084.
%C A216194 The first n for which a(n)=10 is 28.  The second is 243.
%C A216194 The first n for which a(n)=11 is 31.  The second is 58130496.
%C A216194 a(n)<=11 for all n with fewer than 3000 base 10 digits.  No n for which a(n)>11 has been found.
%H A216194 Nathan Fox, <a href="/A216194/b216194.txt">Table of n, a(n) for n = 1..10000</a>
%p A216194 firstNTerms:=proc(n) local b,i,rep,L:
%p A216194 L:=[]:
%p A216194 for i from 5 to n do
%p A216194     b:=3:
%p A216194     while true do
%p A216194         rep:=convert(i, base, b):
%p A216194         if evalb(2 in rep) then
%p A216194             L:=[op(L), b]:
%p A216194             break:
%p A216194         fi:
%p A216194         b:=b+1:
%p A216194     od:
%p A216194 od:
%p A216194 L:
%p A216194 end:
%t A216194 sb2[n_]:=Module[{b=3},While[DigitCount[n,b,2]<1,b++];b]; Array[sb2,110,5] (* _Harvey P. Dale_, Jan 16 2016 *)
%t A216194 Table[SelectFirst[Range[3, 1200], DigitCount[n, #, 2] > 0 &], {n, 5, 120}] (* _Michael De Vlieger_, Mar 09 2016, Version 10 *)
%o A216194 (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 A216194 Cf. A216192, A270027, A270028, A270029, A270030, A270031, A270032, A270033, A270034, A270035.
%K A216194 nonn,easy,base
%O A216194 1,2
%A A216194 _Nathan Fox_, Mar 12 2013
%E A216194 Modified the definition to make the offset 1 by _Nathan Fox_, Mar 10 2016