

A326699


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


7



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
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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: A073078 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



