cp's OEIS Frontend

A385507 a(n) = v(1 + F(2*n - 1)), where F(x) = (3*x + 1)/2^v(3*x + 1), x is any odd natural number, and v(y) is the 2-adic valuation of y.

%I A385507 #20 Jul 24 2025 05:10:08
%S A385507 1,1,1,2,3,1,1,3,1,1,1,2,2,1,2,4,1,1,3,2,5,1,1,3,1,1,1,2,2,1,3,5,1,1,
%T A385507 1,2,3,1,1,3,1,1,1,2,2,1,2,4,1,1,2,2,4,1,1,3,1,1,2,2,2,1,4,6,1,1,1,2,
%U A385507 3,1,1,3,1,1,3,2,2,1,2,4
%N A385507 a(n) = v(1 + F(2*n - 1)), where F(x) = (3*x + 1)/2^v(3*x + 1), x is any odd natural number, and v(y) is the 2-adic valuation of y.
%H A385507 Amiram Eldar, <a href="/A385507/b385507.txt">Table of n, a(n) for n = 1..10000</a>
%F A385507 a(2n) = A001511(n).
%F A385507 a(4n-3) = A001511(3n-2).
%F A385507 a(4n-1) = a(n).
%F A385507 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2. - _Amiram Eldar_, Jul 23 2025
%t A385507 v[y_] := IntegerExponent[y, 2]; f[x_] := (3*x + 1)/2^v[3*x + 1]; Table[v[1 + f[2*k -1]], {k, 73}]
%o A385507 (PARI) F(x) = (3*x + 1)/2^valuation(3*x + 1, 2);
%o A385507 a(n) = valuation(1 + F(2*n - 1), 2); \\ _Michel Marcus_, Jul 01 2025
%Y A385507 Cf. A001511, A338199.
%K A385507 nonn
%O A385507 1,4
%A A385507 _Hugo Leeney_, Jul 01 2025