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A228776
Positions of even terms of A050376.
0
1, 3, 9, 63, 6605, 203286826, 425656284238504569
OFFSET
1,2
FORMULA
For n>=2, a(n) = a(n-1) + pi(2^(2^(n-1))), where pi(x) is the prime counting function; for s>1, Product_{n>=1} (1 + A050376(a(n))^(-s)) = 2^s/(2^s-1).
A generalization. Let p be a prime. Let for n>=1 the sequence {a^(p)(n)} be sequence of places of terms of A050376 divisible by p. Then, for n>=2, a^(p)(n) = a^(p)(n-1) + pi(p^(2^(n-1))); for s>1, Product_{n>=1} (1 + A050376(a^(p)(n))^(-s)) = p^s/(p^s-1).
MATHEMATICA
a[1] = 1; a[n_] := a[n] = a[n - 1] + PrimePi[2^(2^(n - 1))]; Array[a, 6] (* Amiram Eldar, Dec 04 2018 *)
PROG
(PARI) a(n) = if (n==1, 1, a(n-1) + primepi(2^(2^(n-1)))); \\ Michel Marcus, Dec 04 2018
CROSSREFS
Cf. A050376.
Sequence in context: A091760 A144525 A276535 * A087673 A046239 A093351
KEYWORD
nonn,more
AUTHOR
Vladimir Shevelev, Sep 04 2013
EXTENSIONS
a(7) from Jinyuan Wang, Mar 03 2020
STATUS
approved