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A224789 Primes p such that both p + nextprime(p) + 1 and p*nextprime(p) + 2 are primes. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 2 09:21 EDT 2020. Contains 335398 sequences. (Running on oeis4.)