A339504 - OEIS

%I #13 Dec 08 2020 02:06:45

%S 11,47,107,587,3467,7499,10799,17327,62207,71147,137387,225227,355007,

%T 442367,504299,554699,874799,961067,1175627,1486847,1512299,1529387,

%U 2617067,2999999,3525167,3538187,3629999,4009007,4148927,4494527,5116907,5338667,5467499,8108207,8227007,10090667,10156799

%N Primes (p*(p+2)-2)/3 for p in A339503.

%C Primes of the form (p*(p+2)-2)/3 where p and p+2 are primes.

%C Primes q such that sqrt(3*q+3)-1 and sqrt(3*q+3)+1 are prime.

%H Robert Israel, <a href="/A339504/b339504.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3)=107 is a term because 107=(17*19-2)/3 with 17, 17+2=19 and 107 all prime.

%p P:= {seq(ithprime(i), i=3..10000)}:

%p T:= P intersect map(`-`, P, 2):

%p select(isprime, map(p -> (p*(p+2)-2)/3, T));

%t Select[Map[(# (# + 2) - 2)/3 &, Select[Prime@ Range[3, 750], PrimeQ[# + 2] &]], PrimeQ] (* _Michael De Vlieger_, Dec 07 2020 *)

%Y Cf. A001359, A339503.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Dec 07 2020