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
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
a[n_] := IntegerExponent[2*n, 4] + 1; Array[a, 100] (* Amiram Eldar, May 22 2023 *)
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PARI
a(n) = valuation(2*n, 4) + 1;
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Python
def A363228(n): return (~n&n-1).bit_length()+3>>1 # Chai Wah Wu, Jul 09 2023
Formula
a(n) = floor(A090739(n)/2).
a(n) = A244415(n) + 1.
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
Comments