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A234649
Difference between the first members of the widest and the narrowest prime pair having an arithmetic mean of n.
1
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.
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
KEYWORD
nonn
AUTHOR
Ralf Stephan, Dec 29 2013
STATUS
approved