A127350 a(n) = Sum_{i=n..n+3}Sum_{j=i+1..n+4}prime(i)*prime(j).

288, 574, 1078, 1750, 2710, 4006, 5590, 7630, 10270, 13030, 15766, 19462, 23510, 27550, 32830, 38590, 43750, 49190, 55570, 62302, 70726, 80470, 89350, 98710, 106870, 113590, 124822, 137590, 151990, 167230, 186454, 199798, 214774, 230270

Offset

1,1

Comments

a(n) = absolute value of the coefficient of x^3 of the polynomial Prod_{j=0,4}(x-prime(n+j)) of degree 5; the roots of this polynomial are prime(n), ..., prime(n+4); cf. Vieta's formulas.

All terms are even.

Links

Table of n, a(n) for n=1..34.

Eric Weisstein's World of Mathematics, Vieta's Formulas

Mathematica

Table[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], {x, 1, 100}]

Prog

(PARI) 1. {m=34; k=4; for(n=1, m, print1(sum(i=n, n+k-1, sum(j=i+1, n+k, prime(i)*prime(j))), ", "))} 2. {m=34; k=4; for(n=1, m, print1(abs(polcoeff(prod(j=0, k, (x-prime(n+j))), 3)), ", "))} - Klaus Brockhaus, Jan 21 2007

Crossrefs

Cf. A127345, A127346, A127347, A127348, A127349, A127351, A070934, A006094.

Sequence in context: A061831 A250774 A082994 * A158253 A292054 A250788

Adjacent sequences: A127347 A127348 A127349 * A127351 A127352 A127353

Keyword

nonn

Author

Artur Jasinski, Jan 11 2007

Extensions

Edited by Klaus Brockhaus, Jan 21 2007

Status

approved