A157722 Primes of the Form : p1=a*b+c;p2=a*c+b;p3=b*c+a;p=(p1+p2+p3)/2; p1,p2 and p3 are three consecutive prime numbers.

43, 863, 1181, 3467, 10613, 23081, 26189, 27803, 42407, 138731, 463949, 630167, 702101, 1038731, 1417649, 1452851, 2005061, 2060921, 4925861, 6565721, 9709163, 9739721, 10047881, 14268113, 15515573, 16575113, 16615031, 17300873, 17382461

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Mathematica

lst={}; Do[a=Prime[n]; b=Prime[n+1]; c=Prime[n+2]; x=a*b+c; y=a*c+b; z=b*c+a; p=(x+y+z)/2; If[PrimeQ[p], AppendTo[lst, p]], {n, 1, 7!}]; lst
prf[{a_, b_, c_}]:=Module[{x=a*b+c, y=b*c+a, z=a*c+b, k}, k=(x+y+z)/2; If[PrimeQ[ k], k, 0]]; DeleteCases[prf/@Partition[Prime[Range[500]], 3, 1], 0] (* Harvey P. Dale, May 12 2016 *)

Crossrefs

Sequence in context: A337904 A278174 A332910 * A010959 A161668 A162181

Adjacent sequences: A157719 A157720 A157721 * A157723 A157724 A157725

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Mar 04 2009

Status

approved