login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A338776 a(n) = card(GB(2*n)), where GB(n) is the set of primes which are Goldbach-associated with n. 2
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 (list; graph; refs; listen; history; text; internal format)
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 * A198325 A293909 A002850

Adjacent sequences:  A338773 A338774 A338775 * A338777 A338778 A338779

KEYWORD

nonn

AUTHOR

Peter Luschny, Nov 08 2020

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 18 10:19 EDT 2021. Contains 343995 sequences. (Running on oeis4.)