A326700 Denominator of the average position of a 1 in the reversed binary expansion of n.

1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 3, 2, 3, 1, 2, 1, 1, 2, 3, 1, 1, 3, 4, 2, 3, 3, 1, 1, 4, 2, 1, 1, 2, 1, 1, 2, 3, 3, 1, 1, 3, 1, 4, 3, 2, 4, 5, 2, 1, 3, 2, 3, 4, 1, 5, 1, 1, 4, 5, 2, 5, 1, 2, 1, 1, 2, 3, 1, 3, 1, 4, 2, 1, 3, 2, 3, 4, 1, 5, 1, 3, 3, 4, 1, 1, 4, 5

Offset

1,3

Comments

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) = 2.

a(n) divides A000120(n). - Robert Israel, Oct 07 2019

Links

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

Maple

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

Mathematica

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

Crossrefs

Positions of 1's are A326669.

Cf. A000120, A029931, A035327, A048793, A070939, A291166, A295235, A326674, A326699 (numerators).

Sequence in context: A067760 A078680 A296072 * A050412 A307017 A220424

Adjacent sequences: A326697 A326698 A326699 * A326701 A326702 A326703

Keyword

nonn,frac

Author

Gus Wiseman, Jul 20 2019

Status

approved