OFFSET
1,1
COMMENTS
Composites of the form prime(k)*prime(k+1)+prime(k)*prime(k+2)+prime(k+1)*prime(k+2).
A composite number n is in the sequence if for some k it is the coefficient of x^1 of the polynomial Prod_{j=0..2}(x-prime(k+j)); the roots of this polynomial are prime(k), ..., prime(k+2).
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
MATHEMATICA
b = {}; a = {}; Do[If[PrimeQ[Prime[x] Prime[x + 1] + Prime[x] Prime[x + 2] + Prime[x + 1] Prime[x + 2]], AppendTo[a, Prime[x] Prime[x + 1] + Prime[x] Prime[x + 2] + Prime[x + 1] Prime[x + 2]], AppendTo[b, Prime[x] Prime[x + 1] + Prime[x] Prime[x + 2] + Prime[x + 1] Prime[x + 2]]], {x, 1, 100}]; Print[a]; Print[b]
Select[Total[Times@@@Subsets[#, {2}]]&/@Partition[Prime[ Range[80]], 3, 1], !PrimeQ[#]&] (* Harvey P. Dale, May 27 2012 *)
PROG
(PARI) {m=52; k=2; for(n=1, m, a=sum(i=n, n+k-1, sum(j=i+1, n+k, prime(i)*prime(j))); if(!isprime(a), print1(a, ", ")))} \\ Klaus Brockhaus, Jan 21 2007
(PARI) {m=52; k=2; for(n=1, m, a=polcoeff(prod(j=0, k, (x-prime(n+j))), 1); if(!isprime(a), print1(a, ", ")))} \\ Klaus Brockhaus, Jan 21 2007
CROSSREFS
KEYWORD
nonn
AUTHOR
Artur Jasinski, Jan 11 2007
EXTENSIONS
Edited and extended by Klaus Brockhaus, Jan 21 2007
STATUS
approved