|
|
A228776
|
|
Positions of even terms of A050376.
|
|
0
|
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
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
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|