A327491 a(0) = 0. If 4 divides n then a(n) = valuation(n, 2) else a(n) = (n mod 2) + 1.

0, 2, 1, 2, 2, 2, 1, 2, 3, 2, 1, 2, 2, 2, 1, 2, 4, 2, 1, 2, 2, 2, 1, 2, 3, 2, 1, 2, 2, 2, 1, 2, 5, 2, 1, 2, 2, 2, 1, 2, 3, 2, 1, 2, 2, 2, 1, 2, 4, 2, 1, 2, 2, 2, 1, 2, 3, 2, 1, 2, 2, 2, 1, 2, 6, 2, 1, 2, 2, 2, 1, 2, 3, 2, 1, 2, 2, 2, 1, 2, 4, 2, 1, 2, 2, 2, 1, 2

Offset: 0

Author

Peter Luschny, Sep 27 2019

Keywords

• nonn

Examples

			Seen as an irregular table for n >= 1:
  2,
  1, 2,
  2, 2, 1, 2,
  3, 2, 1, 2, 2, 2, 1, 2,
  4, 2, 1, 2, 2, 2, 1, 2, 3, 2, 1, 2, 2, 2, 1, 2,
  5, 2, 1, 2, 2, 2, 1, 2, 3, 2, 1, 2, 2, 2, 1, 2, 4, 2, 1, 2, ....
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A327492, A327493, A327494, A327495.

Programs

Maple

A327491 := n -> if n = 0 then 0
elif 0 = irem(n, 4) then padic[ordp](n, 2)
elif 0 = irem(n, 2) then 1 else 2 fi:
seq(A327491(n), n=0..87);

Mathematica

a[0] = 0; a[n_] := If[Divisible[n, 4], IntegerExponent[n, 2], Mod[n, 2] + 1]; Array[a, 100, 0] (* Amiram Eldar, Aug 30 2024 *)

PARI

a(n)={if(n==0, 0, if(n%4, n%2 + 1, valuation(n,2)))} \\ Andrew Howroyd, Sep 28 2019

SageMath

def A327491(n):
    if n == 0: return 0
    if 4.divides(n): return valuation(n, 2)
    return n % 2 + 1
print([A327491(n) for n in (0..87)])

Formula

a(0) = 0; if n is odd then a(n) = 2, otherwise a(n) = A007814(n). - Andrey Zabolotskiy, Jan 08 2024

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2. - Amiram Eldar, Aug 30 2024