A127351 - OEIS

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

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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