cp's OEIS Frontend

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

%I A341550 #16 Mar 23 2021 02:54:02
%S A341550 29,103,1229,2609,3733,4229,4903,11239,21013,47507,65033,73453,75629,
%T A341550 105601,112241,132499,172213,257069,330641,361213,379459,570029,
%U A341550 667477,893033,950633,976147,1054717,1240999,1435219,1934837,2149151,2775559,2829011,3189799
%N A341550 Primes of the form prime(i)*prime(i+1)+2*prime(i+2).
%C A341550 Conjecture: sequence is infinite.
%C A341550 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
%H A341550 Robert Israel, <a href="/A341550/b341550.txt">Table of n, a(n) for n = 1..10000</a>
%e A341550 3*5+2*7 = 29 which is prime and so is a(1).
%e A341550 5*7+2*11 = 57 which is composite and so not in the sequence.
%p A341550 R:= NULL: count:= 0: q:= 2: r:= 3;
%p A341550 while count < 100 do
%p A341550   p:= q; q:= r; r:=nextprime(r);
%p A341550   x:= p*q+2*r;
%p A341550   if isprime(x) then
%p A341550      count:= count+1; R:= R, x;
%p A341550   fi
%p A341550 od:
%p A341550 R; # _Robert Israel_, Mar 22 2021
%t A341550 Select[#1*#2 + 2*#3 & @@@ Partition[Select[Range[2000], PrimeQ], 3, 1], PrimeQ] (* _Amiram Eldar_, Feb 16 2021 *)
%o A341550 (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;}
%Y A341550 Cf. A000040, A180945.
%K A341550 nonn,easy
%O A341550 1,1
%A A341550 _Bill McEachen_, Feb 14 2021