A234649 Difference between the first members of the widest and the narrowest prime pair having an arithmetic mean of n.

2, 2, 4, 2, 6, 4, 6, 6, 10, 8, 12, 0, 14, 14, 10, 14, 14, 16, 18, 16, 16, 12, 22, 16, 20, 24, 24, 26, 26, 28, 26, 32, 30, 26, 36, 16, 36, 36, 28, 36, 36, 18, 44, 38, 40, 44, 42, 40, 50, 48, 40, 42, 52, 30, 42, 46, 42, 56, 56, 58, 48, 60, 64, 56, 66, 60, 48, 60, 70, 68, 68, 54, 68, 74, 60, 56

Offset

8,1

Comments

The widest prime pair with a mean of n is (A002373(n),A020482(n)) and the narrowest is (A078587(n),A078496(n)).

Existence of a(n) for all n depends on A061357(n) > 0.

Even numbers missing in the subsequence with n<10^5 are 34,62,82,88,112,116,118,122,130,140,152...

a(n) = 0 for n=4,5,6,7,19 because A061357(n) = 1.

Links

Ralf Stephan, Table of n, a(n) for n = 8..100000

Formula

a(n) = A078587(n) - A002373(n) = A078496(n) - A020482(n).

Example

The prime pairs with an arithmetic mean of 18 are (17,19), (13,23), (7,29), and (5,31), so a(18) = 17-5 = 31-19 = 12. The only pair with mean of 19 is (7,31) so a(19) = 0.

Prog

(PARI) a(n)=mi=0; ma=0; forprime(p=3, n-1, if(isprime(2*n-p), if(!mi, mi=2*n-p); ma=2*n-p)); if(!ma, -1, mi-ma)

Crossrefs

Cf. A045917.

Sequence in context: A028496 A063428 A133439 * A072300 A210359 A286553

Adjacent sequences: A234646 A234647 A234648 * A234650 A234651 A234652

Keyword

nonn

Author

Ralf Stephan, Dec 29 2013

Status

approved