A127351 Prime numbers n such that A127350(k) = 2*n for some k.

2003, 7883, 31151, 35363, 394739, 434939, 541007, 564983, 837929, 865979, 2453999, 2680493, 3479303, 3536219, 4145717, 4367267, 4706311, 5414159, 6541103, 6856019, 8804231, 9109223, 10227323, 10296059, 10701683, 10795507

Offset: 1

Author

Artur Jasinski, Jan 11 2007

Keywords

• nonn

Comments

Primes of the form (Sum_{i=k..k+3}Sum_{j=i+1..k+4}prime(i)*prime(j))/2.

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.

Crossrefs

Cf. A127350, A127345, A127346, A127347, A127348, A127349, A070934, A006094.

Programs

Mathematica

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

PARI

{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,",")))} \\ Klaus Brockhaus, Jan 21 2007

PARI

{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

Extensions

Edited by Klaus Brockhaus, Jan 21 2007