A127347 Composites in A127345.

551, 791, 1655, 2279, 3935, 8391, 9959, 11639, 13175, 16559, 18383, 20975, 27419, 30191, 32231, 36071, 40511, 45791, 51983, 55199, 64199, 69599, 73911, 84311, 89751, 94679, 112511, 122759, 133419, 145571, 153671, 163775, 169439, 178079

Offset: 1

Author

Artur Jasinski, Jan 11 2007

Keywords

• nonn

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

Crossrefs

Cf. A127345, A127346, A127347.

Programs

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 *)

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

Extensions

Edited and extended by Klaus Brockhaus, Jan 21 2007