A371908 - OEIS

A371908

a(n) = 2-adic valuation of A008336(2*n).

0, 1, 3, 2, 5, 4, 2, 1, 5, 4, 2, 1, 4, 3, 1, 0, 5, 4, 2, 1, 4, 3, 1, 0, 4, 3, 1, 0, 3, 2, 0, 1, 7, 6, 4, 3, 0, 1, 3, 2, 6, 5, 3, 2, 5, 4, 2, 1, 6, 5, 3, 4, 1, 0, 2, 1, 5, 4, 2, 1, 4, 3, 1, 0, 7, 6, 4, 3, 0, 1, 3, 2, 6, 5, 3, 2, 5, 4, 2, 1, 6, 5, 3, 2, 5, 4, 2

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OFFSET

1,3

COMMENTS

Aside from initial 0, first 50 terms agree with A371905: A371905(50) = 3 while a(51) = 5.

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A007814(A008336(2*n)).

EXAMPLE

Let b(n) = A008336(n) and let f(x) = A007814(x).

a(1) = 0 since b(2*1) = 1 and f(b(2)) = 0.

a(2) = 1 since b(2*2) = 6 and f(b(4)) = 1.

a(3) = 3 since b(2*3) = 120 and f(b(6)) = 3, etc.

MATHEMATICA

k = 1; nn = 240; p[_] := 0; r = 0; q = Prime[k];

{0}~Join~Reap[

Do[If[AnyTrue[#, p[#1] < #2 & @@ # &],

Map[p[#1] += #2 & @@ # &, #],

Map[p[#1] -= #2 & @@ # &, #] ] &@

Map[{PrimePi[#1], #2} & @@ # &, FactorInteger[n]];

If[Divisible[n, q], Sow[p[k] ] ], {n, nn}] ][[-1, 1]]

PROG

(Python)

from itertools import count, islice

def A371908_gen(): # generator of terms

m = 1

for n in count(1, 2):

a, b = divmod(m, n)

m = m*n if b else a

yield (~m&m-1).bit_length()

a, b = divmod(m, n+1)

m = m*(n+1) if b else a

A371908_list = list(islice(A371908_gen(), 20)) # Chai Wah Wu, Apr 15 2024

CROSSREFS

Cf. A007814, A008336, A371905, A372095, A372840.

Sequence in context: A343782 A363447 A371905 * A143956 A110661 A143124

Adjacent sequences: A371905 A371906 A371907 * A371909 A371910 A371911

KEYWORD

nonn,easy

AUTHOR

Michael De Vlieger, Apr 11 2024

STATUS

approved