A317909 - OEIS

%I #18 Aug 16 2018 16:06:25

%S 5,11,23,29,59,97,109,137,139,149,197,257,263,269,283,293,317,347,359,

%T 421,431,569,587,593,601,617,643,647,653,677,683,691,709,761,797,809,

%U 839,881,947,977,983,1091,1163,1213,1237,1259,1361,1373

%N Primes p such that prime(p) + p + 1 is prime.

%C It appears that the resulting primes are a subsequence of A112885. - _Michel Marcus_, Aug 16 2018

%C If p is a prime in this sequence, then prime(p)+p+1 is prime. Put k = p+1, then prime(p)+p+1 = prime(k-1)+k, and is prime, so is in A112885. Therefore the resulting primes of this sequence are a subsequence of A112885. - _David James Sycamore_, Aug 16 2018

%H Giovanni Resta, <a href="/A317909/b317909.txt">Table of n, a(n) for n = 1..10000</a>

%e Prime(5)+5+1 = 11+5+1 = 17 therefore 5 is a member of the sequence, and is the first such prime, hence a(1) = 5.

%p N := 2000;

%p for X from 1 to N do

%p Z := ithprime(X);

%p P := Z+X+1;

%p if isprime(X) and isprime(P) then print(X);

%p end if

%p end do

%t Select[Prime@ Range@ 300, PrimeQ[# + Prime[#] + 1] &] (* _Giovanni Resta_, Aug 16 2018 *)

%o (PARI) isok(p) = isprime(p) && isprime(prime(p) + p + 1); \\ _Michel Marcus_, Aug 16 2018

%Y Cf. A112885.

%K nonn

%O 1,1

%A _David James Sycamore_, Aug 10 2018