A326700 - OEIS

%I #11 Oct 07 2019 19:58:09

%S 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,

%T 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,

%U 3,1,4,2,1,3,2,3,4,1,5,1,3,3,4,1,1,4,5

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

%C 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.

%C 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.

%C a(n) divides A000120(n). - _Robert Israel_, Oct 07 2019

%H Robert Israel, <a href="/A326700/b326700.txt">Table of n, a(n) for n = 1..10000</a>

%p f:= proc(n) local L;

%p   L:= convert(n,base,2);

%p   L:= select(t -> L[t]=1, [$1..nops(L)]);

%p   denom(convert(L,`+`)/nops(L))

%p end proc:

%p map(f, [$1..100]); # _Robert Israel_, Oct 07 2019

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

%Y Positions of 1's are A326669.

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

%K nonn,frac

%O 1,3

%A _Gus Wiseman_, Jul 20 2019