A128550 a(n) = p, the lesser of twin primes (p, q=p+2) such that p*q + p + q is prime.

3, 5, 11, 17, 41, 59, 101, 137, 311, 419, 521, 809, 1019, 1049, 1151, 1229, 1319, 1427, 2111, 2237, 2267, 3119, 3329, 3371, 3539, 4001, 4049, 4091, 4217, 4421, 4721, 5009, 6359, 6569, 6689, 6761, 7487, 7949, 8537, 8627, 9629, 9719, 10007, 10091, 10709

Offset

1,1

Comments

Or, primes p such that p+2 and 2 + 4*p + p^2 are prime.

Links

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

Example

3, 5 and 3*5+3+5=23 are prime; 5, 7 and 5*7+5+7=47 are prime; 11, 13 and 11*13+11+13 are primes.

Mathematica

lst={}; Do[p=Prime[n]; r=p+2; If[PrimeQ[r], If[PrimeQ[p*r+p+r], AppendTo[lst, p]]], {n, 8!}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 28 2009 *)
Transpose[Select[Select[Partition[Prime[Range[1500]], 2, 1], #[[2]]- #[[1]] == 2&], PrimeQ[Times@@#+Total[#]]&]][[1]] (* Harvey P. Dale, Aug 24 2014 *)

Prog

(PARI) is(n)=isprime(n)&&isprime(n+2)&&isprime(n^2+4*n+2) \\ Charles R Greathouse IV, Jan 29 2013

Crossrefs

Cf. A096342, A126148, A128547, A128548, A128551.

Sequence in context: A034729 A115786 A252089 * A096479 A129809 A208572

Adjacent sequences: A128547 A128548 A128549 * A128551 A128552 A128553

Keyword

nonn

Author

Zak Seidov, Mar 10 2007

Status

approved