A216411 Number of bases in which n begins with a "1".

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, 19, 19, 20, 19, 20, 20, 21, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 30, 29, 30, 30, 31, 30, 31, 31, 32, 32, 33, 33, 34, 34, 35, 37, 38, 38, 39, 39, 40, 40

Offset: 2

Author

Will Nicholes, Sep 07 2012

Keywords

• nonn
• base

Comments

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.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 2..10000

Programs

Mathematica

Table[Length[Select[Range[2, n], IntegerDigits[n, #][[1]] == 1 &]], {n, 2, 100}] (* T. D. Noe, Sep 07 2012 *)

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

Formula

a(n) = n/2 + O(sqrt(n)). - Charles R Greathouse IV, Sep 07 2012