login
A371908
a(n) = 2-adic valuation of A008336(2*n).
3
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
OFFSET
1,3
COMMENTS
Aside from initial 0, first 50 terms agree with A371905: A371905(50) = 3 while a(51) = 5.
LINKS
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
KEYWORD
nonn,easy
AUTHOR
Michael De Vlieger, Apr 11 2024
STATUS
approved