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

1,1

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.

Links

Table of n, a(n) for n=1..26.

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

Prog

(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

Crossrefs

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

Sequence in context: A108116 A140920 A162240 * A162241 A162243 A203043

Adjacent sequences: A127348 A127349 A127350 * A127352 A127353 A127354

Keyword

nonn

Author

Artur Jasinski, Jan 11 2007

Extensions

Edited by Klaus Brockhaus, Jan 21 2007

Status

approved