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

0,10

Comments

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.

Links

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

Formula

a(n) <= A002375(n).

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

Example

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]

Prog

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

Crossrefs

Cf. A338777, A002375, A244408.

Sequence in context: A248218 A182110 A175328 * A345933 A198325 A293909

Adjacent sequences: A338773 A338774 A338775 * A338777 A338778 A338779

Keyword

nonn

Author

Peter Luschny, Nov 08 2020

Status

approved