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 A338776 #14 Nov 09 2020 08:35:06 %S A338776 0,0,0,1,1,1,1,1,1,2,1,2,3,2,1,3,1,2,3,2,2,3,2,2,4,2,2,4,2,3,5,2,3,4, %T A338776 1,4,5,3,3,5,3,4,7,3,3,8,3,4,6,3,5,7,3,4,6,4,5,8,4,5,11,4,4,10,3,6,8, %U A338776 4,4,6,6,5,9,5,4,11,3,6,9,4,6,8,4,5,11 %N A338776 a(n) = card(GB(2*n)), where GB(n) is the set of primes which are Goldbach-associated with n. %C A338776 For an integer n >= 0 we say a prime p is gb-associated with n if sqrt(n) < p <= n/2 and no prime q which is <= sqrt(n) divides p*(p - n). Let GB(n) be the set of integers which are gb-associated with n (for examples see A338777). a(n) is the number of primes which are gb-associated with n. %C A338776 If a(n) > 0 for n >= 3 then Goldbach's conjecture is true. %H A338776 Peter Luschny, <a href="/A338776/b338776.txt">Table of n, a(n) for n = 0..1000</a> %F A338776 a(n) <= A002375(n). %F A338776 a(n) = A002375(n) <=> n in A244408 (for n >= 2). %e A338776 Comparison of the sets whose cardinality is given by A002375(n) resp. a(n). %e A338776 m A002375 A338776 %e A338776 32 [29, 19] [19] %e A338776 34 [31, 29, 23, 17] [23, 17] %e A338776 36 [31, 29, 23, 19] [29, 23, 19] %e A338776 38 [31, 19] [31, 19] %o A338776 (SageMath) # [using gb_associated from A338777] %o A338776 def A338776(n): %o A338776 return len(gb_associated(2*n)) %o A338776 print([A338776(n) for n in range(87)]) %Y A338776 Cf. A338777, A002375, A244408. %K A338776 nonn %O A338776 0,10 %A A338776 _Peter Luschny_, Nov 08 2020