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.

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, 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, 3, 1, 1, 3, 1, 1, 3, 2, 2, 1, 2, 4

Offset

1,4

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(2n) = A001511(n).

a(4n-3) = A001511(3n-2).

a(4n-1) = a(n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2. - Amiram Eldar, Jul 23 2025

Mathematica

v[y_] := IntegerExponent[y, 2]; f[x_] := (3*x + 1)/2^v[3*x + 1]; Table[v[1 + f[2*k -1]], {k, 73}]

Prog

(PARI) F(x) = (3*x + 1)/2^valuation(3*x + 1, 2);
a(n) = valuation(1 + F(2*n - 1), 2); \\ Michel Marcus, Jul 01 2025

Crossrefs

Cf. A001511, A338199.

Sequence in context: A308297 A251045 A300521 * A356152 A317627 A271566

Adjacent sequences: A385504 A385505 A385506 * A385508 A385509 A385510

Keyword

nonn

Author

Hugo Leeney, Jul 01 2025

Status

approved