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%I #18 Jan 06 2014 14:56:58
%S 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,
%T 24,26,26,28,26,32,30,26,36,16,36,36,28,36,36,18,44,38,40,44,42,40,50,
%U 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
%N Difference between the first members of the widest and the narrowest prime pair having an arithmetic mean of n.
%C The widest prime pair with a mean of n is (A002373(n),A020482(n)) and the narrowest is (A078587(n),A078496(n)).
%C Existence of a(n) for all n depends on A061357(n) > 0.
%C Even numbers missing in the subsequence with n<10^5 are 34,62,82,88,112,116,118,122,130,140,152...
%C a(n) = 0 for n=4,5,6,7,19 because A061357(n) = 1.
%H Ralf Stephan, <a href="/A234649/b234649.txt">Table of n, a(n) for n = 8..100000</a>
%F a(n) = A078587(n) - A002373(n) = A078496(n) - A020482(n).
%e 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.
%o (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)
%Y Cf. A045917.
%K nonn
%O 8,1
%A _Ralf Stephan_, Dec 29 2013