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%I #4 Mar 31 2012 10:22:03
%S 2003,7883,31151,35363,394739,434939,541007,564983,837929,865979,
%T 2453999,2680493,3479303,3536219,4145717,4367267,4706311,5414159,
%U 6541103,6856019,8804231,9109223,10227323,10296059,10701683,10795507
%N Prime numbers n such that A127350(k) = 2*n for some k.
%C Primes of the form (Sum_{i=k..k+3}Sum_{j=i+1..k+4}prime(i)*prime(j))/2.
%C Primes of the form a/2 where a is the coefficient of x^3 of the polynomial Prod_{j=0,4}(x-prime(k+j)) for some k.
%t a = {}; Do[If[PrimeQ[(Prime[x] Prime[x + 1] + Prime[x] Prime[x + 2] + Prime[x] Prime[x + 3] + Prime[x] Prime[x + 4] + Prime[x + 1] Prime[x + 2] + Prime[x + 1] Prime[x + 3] + Prime[x + 1] Prime[x + 4] + Prime[x + 2] Prime[x + 3] + Prime[x + 2] Prime[x + 4] + Prime[x + 3] Prime[x + 4])/2], AppendTo[a, (Prime[x] Prime[x + 1] + Prime[x] Prime[x + 2] + Prime[x] Prime[x + 3] + Prime[x] Prime[x + 4] + Prime[x + 1] Prime[x + 2] + Prime[x + 1] Prime[x + 3] + Prime[x + 1] Prime[x + 4] + Prime[x + 2] Prime[x + 3] + Prime[x + 2] Prime[x + 4] + Prime[x + 3] Prime[x + 4])/2]], {x, 1, 1000}]; a
%o (PARI) 1. {m=235;k=4;for(n=1,m,a=sum(i=n,n+k-1,sum(j=i+1,n+k,prime(i)*prime(j)));if(isprime(b=a/2),print1(b,",")))} 2. {m=235;k=4;for(n=1,m,a=polcoeff(prod(j=0,k,(x-prime(n+j))),3);if(isprime(b=a/2),print1(b,",")))} - Klaus Brockhaus, Jan 21 2007
%Y Cf. A127350, A127345, A127346, A127347, A127348, A127349, A070934, A006094.
%K nonn
%O 1,1
%A _Artur Jasinski_, Jan 11 2007
%E Edited by _Klaus Brockhaus_, Jan 21 2007
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