A341550 Primes of the form prime(i)*prime(i+1)+2*prime(i+2).

29, 103, 1229, 2609, 3733, 4229, 4903, 11239, 21013, 47507, 65033, 73453, 75629, 105601, 112241, 132499, 172213, 257069, 330641, 361213, 379459, 570029, 667477, 893033, 950633, 976147, 1054717, 1240999, 1435219, 1934837, 2149151, 2775559, 2829011, 3189799

Offset: 1

Author

Bill McEachen, Feb 14 2021

Keywords

• nonn
• easy

Comments

Conjecture: sequence is infinite.

The generalized Dickson conjecture implies, for example, that there are infinitely many primes p for which p+4, p+6 and p*(p+4)+2*(p+6) = p^2+6*p+12 are prime. - Robert Israel, Mar 22 2021

Examples

			3*5+2*7 = 29 which is prime and so is a(1).
5*7+2*11 = 57 which is composite and so not in the sequence.
		

Links

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

Crossrefs

Cf. A000040, A180945.

Programs

Maple

R:= NULL: count:= 0: q:= 2: r:= 3;
while count < 100 do
  p:= q; q:= r; r:=nextprime(r);
  x:= p*q+2*r;
  if isprime(x) then
     count:= count+1; R:= R, x;
  fi
od:
R; # Robert Israel, Mar 22 2021

Mathematica

Select[#1*#2 + 2*#3 & @@@ Partition[Select[Range[2000], PrimeQ], 3, 1], PrimeQ] (* Amiram Eldar, Feb 16 2021 *)

PARI

genit(maxx)={p=List(); forprime(x=3,maxx,q=nextprime(x+1); w=x*q+2*nextprime(q+1); if(isprime(w),listput(p,w)));p;}