This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A228776 #28 Feb 19 2025 10:27:29
%S A228776 1,3,9,63,6605,203286826,425656284238504569
%N A228776 Positions of even terms of A050376.
%F A228776 For n>=2, a(n) = a(n-1) + pi(2^(2^(n-1))), where pi(x) is the prime counting function.
%F A228776 For s>1, Product_{n>=1} (1 + A050376(a(n))^(-s)) = 2^s/(2^s-1).
%F A228776 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).
%t A228776 a[1] = 1; a[n_] := a[n] = a[n - 1] + PrimePi[2^(2^(n - 1))]; Array[a, 6] (* _Amiram Eldar_, Dec 04 2018 *)
%o A228776 (PARI) a(n) = if (n==1, 1, a(n-1) + primepi(2^(2^(n-1)))); \\ _Michel Marcus_, Dec 04 2018
%o A228776 (Python)
%o A228776 from sympy import primepi
%o A228776 def A228776(n): return sum(primepi(1<<(1<<i)) for i in range(n)) # _Chai Wah Wu_, Feb 18 2025
%Y A228776 Cf. A050376, A153450 (pi(2^(2^(n-1)))).
%K A228776 nonn,more
%O A228776 1,2
%A A228776 _Vladimir Shevelev_, Sep 04 2013
%E A228776 a(6) from _Peter J. C. Moses_
%E A228776 a(7) from _Jinyuan Wang_, Mar 03 2020