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 A385608 #29 Jul 16 2025 10:13:57
%S A385608 0,0,0,1,1,1,4,4,4,5,5,5,9,9,9,10,10,10,13,13,13,14,14,14,19,19,19,20,
%T A385608 20,20,23,23,23,24,24,24,28,28,28,29,29,29,32,32,32,33,33,33,39,39,39,
%U A385608 40,40,40,43,43,43,44,44,44,48,48,48,49,49,49,52,52,52,53,53,53
%N A385608 a(n) = 2-adic valuation of A003266(n).
%H A385608 Paolo Xausa, <a href="/A385608/b385608.txt">Table of n, a(n) for n = 0..10000</a>
%F A385608 a(n) = 2*floor(n/3) + floor(n/6) - A000120(floor(n/3)) (formula by _David Radcliffe_ at A385458).
%F A385608 a(n) = A007814(A003266(n)).
%F A385608 For n >= 1, a(n) = Sum_{k=1..n} A337923(k).
%F A385608 a(3*k) = a(3*k+1) = a(3*k+2), for k >= 0.
%t A385608 A385608[n_] := 2*# + Quotient[n, 6] - DigitSum[#, 2] & [Quotient[n, 3]];
%t A385608 Array[A385608, 100, 0] (* or *)
%t A385608 Join[{0}, Accumulate[IntegerExponent[Fibonacci[Range[99]], 2]]]
%Y A385608 Cf. A000120, A003266, A007814, A385458, A385609.
%Y A385608 Partial sums of A337923.
%K A385608 nonn,easy
%O A385608 0,7
%A A385608 _Paolo Xausa_, Jul 04 2025