OFFSET
1,1
COMMENTS
Primes of the form prime(k)*prime(k+1) + prime(k)*prime(k+2) + prime(k+1)*prime(k+2).
A prime number n is in the sequence if for some k it is the coefficient of x^1 of the polynomial Product_{j=0..2} (x-prime(k+j)); the roots of this polynomial are prime(k), ..., prime(k+2).
LINKS
Zak Seidov, Table of n, a(n) for n = 1..1000
FORMULA
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] (* Artur Jasinski, Jan 11 2007 *)
s[li_] := li[[1]]*(li[[2]]+li[[3]])+li[[2]]*li[[3]]; Select[(s[#]&/@Partition[Prime[Range[100]], 3, 1]), PrimeQ] (* Zak Seidov, Jan 13 2012 *)
PROG
(PARI) {m=143; 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=143; 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
(PARI) p=2; q=3; forprime(r=5, 1e3, if(isprime(t=p*q+p*r+q*r), print1(t", ")); p=q; q=r) \\ Charles R Greathouse IV, Jan 13 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
Artur Jasinski, Jan 11 2007
EXTENSIONS
Edited and extended by Klaus Brockhaus, Jan 21 2007
STATUS
approved