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A326700 Denominator of the average position of a 1 in the reversed binary expansion of n. 7
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 16 04:56 EDT 2021. Contains 345056 sequences. (Running on oeis4.)