A078496 -id:A078496 - cp's OEIS frontend

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

Ralf Stephan, Dec 29 2013

nonn

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.

			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.

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

Cf. A045917.

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)

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

cp's OEIS Frontend

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

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