This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A364213 #9 Jul 15 2023 05:52:30 %S A364213 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 A364213 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 A364213 0,0,0,2,0,0,4,0,0,2,0,0,0,0,2,0,0,0,0 %N A364213 The number of trailing 0's in the canonical representation of n as a sum of distinct Jacobsthal numbers (A280049). %C A364213 The even terms of A007583. %C A364213 This sequence is unbounded. The first position of 2*k is A007583(k) = (2^(2*k+1) + 1)/3. %C A364213 The asymptotic density of the occurrences of (2*k) in this sequence is 3/4^(k+1). %C A364213 The asymptotic mean of this sequence is 2/3 and its asymptotic standard deviation is 4/3. %H A364213 Amiram Eldar, <a href="/A364213/b364213.txt">Table of n, a(n) for n = 1..10000</a> %F A364213 a(n) = A122840(A280049(n)). %F A364213 a(n) = A007583(A003159(n)). %t A364213 Select[IntegerExponent[Range[100], 2], EvenQ] %o A364213 (PARI) select(x->!(x%2), vector(100, i, valuation(i, 2))) %Y A364213 Cf. A007583, A007814, A122840, A280049. %K A364213 nonn,base,easy %O A364213 1,3 %A A364213 _Amiram Eldar_, Jul 14 2023