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

1,2

Links

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

Example

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.

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}]

Crossrefs

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

Sequence in context: A360296 A034799 A008985 * A138652 A323833 A131899

Adjacent sequences: A326696 A326697 A326698 * A326700 A326701 A326702

Keyword

nonn,frac,look

Author

Gus Wiseman, Jul 20 2019

Status

approved