A385609 -id:A385609 - cp's OEIS frontend

A385608 a(n) = 2-adic valuation of A003266(n).

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, 20, 20, 23, 23, 23, 24, 24, 24, 28, 28, 28, 29, 29, 29, 32, 32, 32, 33, 33, 33, 39, 39, 39, 40, 40, 40, 43, 43, 43, 44, 44, 44, 48, 48, 48, 49, 49, 49, 52, 52, 52, 53, 53, 53

Offset: 0

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Paolo Xausa, Jul 04 2025

nonn
easy

Paolo Xausa, Table of n, a(n) for n = 0..10000

Cf. A000120, A003266, A007814, A385458, A385609.

Partial sums of A337923.

A385608[n_] := 2*# + Quotient[n, 6] - DigitSum[#, 2] & [Quotient[n, 3]];
Array[A385608, 100, 0] (* or *)
Join[{0}, Accumulate[IntegerExponent[Fibonacci[Range[99]], 2]]]

a(n) = 2*floor(n/3) + floor(n/6) - A000120(floor(n/3)) (formula by David Radcliffe at A385458).
a(n) = A007814(A003266(n)).
For n >= 1, a(n) = Sum_{k=1..n} A337923(k).
a(3*k) = a(3*k+1) = a(3*k+2), for k >= 0.

cp's OEIS Frontend

A385608 a(n) = 2-adic valuation of A003266(n).

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