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

1,1

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) 1, {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, ", ")))} 2. {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

Cf. A127345, A127346, A127347.

Sequence in context: A285925 A285861 A034282 * A351664 A063877 A204870

Adjacent sequences: A127344 A127345 A127346 * A127348 A127349 A127350

Keyword

nonn

Author

Artur Jasinski, Jan 11 2007

Extensions

Edited and extended by Klaus Brockhaus, Jan 21 2007

Status

approved