A065017 Primes of the form p*q + p + q, where (p, q=p+2) are twin primes.

23, 47, 167, 359, 1847, 3719, 10607, 19319, 97967, 177239, 273527, 657719, 1042439, 1104599, 1329407, 1515359, 1745039, 2042039, 4464767, 5013119, 5148359, 9740639, 11095559, 11377127, 12538679, 16024007, 16410599, 16752647

Offset

1,1

Comments

The resulting prime can never be a twin prime since the odd number preceding it is divisible by three and the following odd number is a perfect square.

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Formula

p^2 + 4*p + 2.

Example

(3*5) + (3+5) = 23.

Mathematica

NextPrim[n_] := Block[ {k = n + 1}, While[ !PrimeQ[k], k++ ]; Return[k]]; k = 1; Do[k = NextPrim[k]; If[ PrimeQ[k + 2], p = k*(k + 2) + 2k + 2; If[ PrimeQ[p], Print[p]]], {n, 1, 700} ]
f[n_]:=Module[{x=Total[n]+Times@@n}, If[PrimeQ[x], x, 0]]; Select[f/@ (Select[Partition[Prime[Range[700]], 2, 1], Last[#]-First[#]==2&]), #!=0&] (* Harvey P. Dale, May 11 2011 *)

Prog

(PARI) { n=p=0; for (m=1, 10^9, p=nextprime(p + 1); if (isprime(q=p + 2) && isprime(a=p*q + p + q), write("b065017.txt", n++, " ", a); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 03 2009

Crossrefs

Cf. A049001, A049002.

Sequence in context: A042050 A139857 A139900 * A140618 A042052 A136030

Adjacent sequences: A065014 A065015 A065016 * A065018 A065019 A065020

Keyword

nonn

Author

Stephan Wagler (stephanwagler(AT)aol.com), Nov 01 2001

Extensions

Offset changed from 0 to 1 by Harry J. Smith, Oct 03 2009

Status

approved