A364213 - OEIS

%I #9 Jul 15 2023 05:52:30

%S 0,0,2,0,0,0,0,2,0,0,4,0,0,2,0,0,0,0,2,0,0,0,0,2,0,0,0,0,2,0,0,4,0,0,

%T 2,0,0,0,0,2,0,0,6,0,0,2,0,0,0,0,2,0,0,4,0,0,2,0,0,0,0,2,0,0,0,0,2,0,

%U 0,0,0,2,0,0,4,0,0,2,0,0,0,0,2,0,0,0,0

%N The number of trailing 0's in the canonical representation of n as a sum of distinct Jacobsthal numbers (A280049).

%C The even terms of A007583.

%C This sequence is unbounded. The first position of 2*k is A007583(k) = (2^(2*k+1) + 1)/3.

%C The asymptotic density of the occurrences of (2*k) in this sequence is 3/4^(k+1).

%C The asymptotic mean of this sequence is 2/3 and its asymptotic standard deviation is 4/3.

%H Amiram Eldar, <a href="/A364213/b364213.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A122840(A280049(n)).

%F a(n) = A007583(A003159(n)).

%t Select[IntegerExponent[Range[100], 2], EvenQ]

%o (PARI) select(x->!(x%2), vector(100, i, valuation(i, 2)))

%Y Cf. A007583, A007814, A122840, A280049.

%K nonn,base,easy

%O 1,3

%A _Amiram Eldar_, Jul 14 2023