A363228 Exponent of 4 in 9^n - 1.

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

Offset

1,2

Comments

Not the same as A147648-without-zeros.

Links

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

Formula

a(n) = floor(A090739(n)/2).

a(n) = A244415(n) + 1.

a(n) = A235127(A024101(n)). - Michel Marcus, May 21 2023

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 5/3. - Amiram Eldar, Jul 13 2023

Conjecture: a(n) = A235127(A000045(6*n)), all other 4-adic 6-sections A235127(A000045(.)) = 0. - R. J. Mathar, Jun 28 2025

From Amiram Eldar, Oct 31 2025: (Start)

Multiplicative with a(2^e) = floor(e+3)/2, and a(p^e) = 1 for an odd prime p.

Dirichlet g.f.: zeta(s) * (1 + 1/2^s - 1/2^(2*s)) / (1 - 1/2^(2*s)). (End)

Mathematica

a[n_] := IntegerExponent[2*n, 4] + 1; Array[a, 100] (* Amiram Eldar, May 22 2023 *)

Prog

(PARI) a(n) = valuation(2*n, 4) + 1;
(Python)
def A363228(n): return (~n&n-1).bit_length()+3>>1 # Chai Wah Wu, Jul 09 2023

Crossrefs

Cf. A007814, A090739, A147648, A244415.

Cf. A000045, A024101, A235127.

Sequence in context: A168580 A356206 A318707 * A235726 A060938 A087942

Adjacent sequences: A363225 A363226 A363227 * A363229 A363230 A363231

Keyword

nonn,easy,mult

Author

Ruud H.G. van Tol, May 21 2023

Status

approved