A338777 -id:A338777 - cp's OEIS frontend

A338776 a(n) = card(GB(2*n)), where GB(n) is the set of primes which are Goldbach-associated with n.

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, 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, 4, 4, 6, 6, 5, 9, 5, 4, 11, 3, 6, 9, 4, 6, 8, 4, 5, 11

Offset: 0

Peter Luschny, Nov 08 2020

nonn

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.

If a(n) > 0 for n >= 3 then Goldbach's conjecture is true.

			Comparison of the sets whose cardinality is given by A002375(n) resp. a(n).
m  A002375          A338776
32 [29, 19]         [19]
34 [31, 29, 23, 17] [23, 17]
36 [31, 29, 23, 19] [29, 23, 19]
38 [31, 19]         [31, 19]

Peter Luschny, Table of n, a(n) for n = 0..1000

Cf. A338777, A002375, A244408.

# [using gb_associated from A338777]
def A338776(n):
    return len(gb_associated(2*n))
print([A338776(n) for n in range(87)])

a(n) <= A002375(n).

a(n) = A002375(n) <=> n in A244408 (for n >= 2).

cp's OEIS Frontend

A338776 a(n) = card(GB(2*n)), where GB(n) is the set of primes which are Goldbach-associated with n.

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