%I #15 Sep 20 2024 12:28:19

%S 551,791,1655,2279,3935,8391,9959,11639,13175,16559,18383,20975,27419,

%T 30191,32231,36071,40511,45791,51983,55199,64199,69599,73911,84311,

%U 89751,94679,112511,122759,133419,145571,153671,163775,169439,178079

%N Composites in A127345.

%C Composites of the form prime(k)*prime(k+1)+prime(k)*prime(k+2)+prime(k+1)*prime(k+2).

%C 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).

%H Harvey P. Dale, <a href="/A127347/b127347.txt">Table of n, a(n) for n = 1..1000</a>

%t 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]

%t Select[Total[Times@@@Subsets[#,{2}]]&/@Partition[Prime[ Range[80]], 3,1],!PrimeQ[#]&] (* _Harvey P. Dale_, May 27 2012 *)

%o (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

%o (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

%Y Cf. A127345, A127346, A127347.

%K nonn

%O 1,1

%A _Artur Jasinski_, Jan 11 2007

%E Edited and extended by _Klaus Brockhaus_, Jan 21 2007