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%I #25 May 13 2013 01:54:22
%S 1,2,3,4,4,5,5,7,7,8,8,9,9,10,11,12,11,12,12,13,13,14,14,16,16,18,18,
%T 19,19,20,19,20,20,21,22,23,23,24,24,25,25,26,26,27,27,28,28,30,29,30,
%U 30,31,30,31,31,32,32,33,33,34,34,35,37,38,38,39,39,40,40
%N Number of bases in which n begins with a "1".
%C 1 begins with "1" in all bases, 2 begins with "1" only in binary ("10" in base 2), 3 begins with "1" in two bases ("11" in base 2, "10" in base 3), etc.
%H Charles R Greathouse IV, <a href="/A216411/b216411.txt">Table of n, a(n) for n = 2..10000</a>
%F a(n) = n/2 + O(sqrt(n)). - _Charles R Greathouse IV_, Sep 07 2012
%t Table[Length[Select[Range[2, n], IntegerDigits[n, #][[1]] == 1 &]], {n, 2, 100}] (* _T. D. Noe_, Sep 07 2012 *)
%o (PARI) a(n)=my(t=1,s,i);for(i=1,log(n)\log(2)+1,s+=floor((n+.5)^(1/i))-floor(((n+.2)/2)^(1/i)));s \\ _Charles R Greathouse IV_, Sep 07 2012
%K nonn,base
%O 2,2
%A _Will Nicholes_, Sep 07 2012
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