A326699 Numerator of the average position of a 1 in the reversed binary expansion of n.

1, 2, 3, 3, 2, 5, 2, 4, 5, 3, 7, 7, 8, 3, 5, 5, 3, 7, 8, 4, 3, 10, 11, 9, 10, 11, 3, 4, 13, 7, 3, 6, 7, 4, 3, 9, 10, 11, 3, 5, 11, 4, 13, 13, 7, 15, 16, 11, 4, 13, 7, 14, 15, 4, 17, 5, 4, 17, 18, 9, 19, 4, 7, 7, 4, 9, 10, 5, 11, 4, 13, 11, 4, 13, 7, 14, 15, 4

Offset: 1

Author

Gus Wiseman, Jul 20 2019

Keywords

• nonn
• frac
• look

Examples

			The sequence of fractions begins: 1, 2, 3/2, 3, 2, 5/2, 2, 4, 5/2, 3, 7/3, 7/2, 8/3, 3, 5/2, 5, 3, 7/2, 8/3, 4.
For example, the reversed binary expansion of 18 is (0,1,0,0,1), and the average of {2,5} is 7/2, so a(18) = 7.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000120, A029931, A035327, A048793, A070939, A291166, A295235, A326669, A326674, A326700 (denominators).

Programs

Maple

f:= proc(n) local L;
  L:= convert(n,base,2);
  L:= select(t -> L[t]=1, [$1..nops(L)]);
  numer(convert(L,`+`)/nops(L))
end proc:
map(f, [$1..100]); # Robert Israel, Oct 07 2019

Mathematica

Table[Numerator[Mean[Join@@Position[Reverse[IntegerDigits[n,2]],1]]],{n,100}]