A224789 Primes p such that both p + nextprime(p) + 1 and p*nextprime(p) + 2 are primes.

5, 7, 13, 19, 67, 229, 269, 307, 313, 401, 439, 613, 643, 863, 1051, 1693, 1783, 1999, 2143, 2239, 2309, 2423, 2549, 2753, 2819, 3037, 3079, 3089, 3361, 3373, 3389, 3677, 3863, 3877, 4139, 4259, 4519, 4663, 4909, 4933, 5323, 5527, 5581, 5849, 6359, 6577

Offset

1,1

Comments

Intersection of A051507 and A177017.

Links

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

Example

5 is a member since 5 + 7 + 1 = 13 and 5 * 7 + 2 = 37 are both primes.

Mathematica

Select[Prime[Range[900]], PrimeQ[# + NextPrime[#] + 1] && PrimeQ[#*NextPrime[#] + 2] &]
npQ[n_]:=Module[{np=NextPrime[n]}, AllTrue[{n+np+1, n*np+2}, PrimeQ]]; Select[ Prime[ Range[900]], npQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 04 2017 *)

Crossrefs

Cf. A051507, A177017.

Sequence in context: A045444 A129782 A080829 * A078884 A314328 A314329

Adjacent sequences: A224786 A224787 A224788 * A224790 A224791 A224792

Keyword

nonn

Author

Jayanta Basu, Apr 17 2013

Status

approved