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A127346 Primes in A127345.

%I A127346 #28 Sep 20 2024 17:08:11
%S A127346 31,71,167,311,1151,3119,4871,5711,6791,14831,24071,33911,60167,79031,
%T A127346 101159,106367,115631,158231,235751,259751,366791,402551,455471,
%U A127346 565919,635711,644951,1124831,1347971,1510799,1547927,1743419,1851671,2048471
%N A127346 Primes in A127345.
%C A127346 Primes of the form prime(k)*prime(k+1) + prime(k)*prime(k+2) + prime(k+1)*prime(k+2).
%C A127346 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).
%H A127346 Zak Seidov, <a href="/A127346/b127346.txt">Table of n, a(n) for n = 1..1000</a>
%F A127346 a(n) = A127345(A204231(n)). - _Zak Seidov_, Jan 13 2012
%t A127346 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 *)
%t A127346 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 *)
%o A127346 (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
%o A127346 (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
%o A127346 (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
%Y A127346 Cf. A127345, A127347, A127351, A006094, A002110, A034962, A034965, A082246, A082251, A127340, A127341, A070934, A046301, A046302, A046303, A046324, A046325, A046326, A046327.
%K A127346 nonn
%O A127346 1,1
%A A127346 _Artur Jasinski_, Jan 11 2007
%E A127346 Edited and extended by _Klaus Brockhaus_, Jan 21 2007