A180931 Primes p such that their product for the successive prime plus one added to one is a prime: p(i)*[p(i+1)+1]+1 gives a prime.

3, 5, 19, 23, 29, 47, 53, 59, 79, 137, 167, 179, 233, 239, 241, 263, 283, 349, 353, 359, 383, 389, 419, 421, 439, 491, 563, 617, 653, 701, 709, 719, 739, 769, 797, 811, 829, 887, 1049, 1051, 1129, 1153, 1187, 1399, 1433, 1489, 1523, 1549, 1559, 1579, 1601

Offset: 1

Author

Carmine Suriano, Sep 26 2010

Keywords

• nonn

Comments

There are some twin primes in the sequence: (3,5); (239,241); (419, 421); (1607, 1609).

Apparently the sequence is infinite.

Examples

			a(5)=29 since 29*(31+1)+1=29*32+1=929 is a prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040.

Programs

Maple

R:= NULL; count:= 0:
q:= 2:
while count < 100 do
  p:= q; q:= nextprime(q);
  if isprime(p*(q+1)+1) then count:= count+1; R:= R, p fi
od:
R; # Robert Israel, May 12 2020

Mathematica

Select[Prime[Range[350]],PrimeQ[ # (NextPrime[ # ]+1)+1]&] (* Harvey P. Dale, Oct 08 2010 *)

Extensions

Added missing terms (5 terms were omitted after 887). Harvey P. Dale, Oct 08 2010