A317909 Primes p such that prime(p) + p + 1 is prime.

5, 11, 23, 29, 59, 97, 109, 137, 139, 149, 197, 257, 263, 269, 283, 293, 317, 347, 359, 421, 431, 569, 587, 593, 601, 617, 643, 647, 653, 677, 683, 691, 709, 761, 797, 809, 839, 881, 947, 977, 983, 1091, 1163, 1213, 1237, 1259, 1361, 1373

Offset

1,1

Comments

It appears that the resulting primes are a subsequence of A112885. - Michel Marcus, Aug 16 2018

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

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Example

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.

Maple

N := 2000;
for X from 1 to N do
Z := ithprime(X);
P := Z+X+1;
if isprime(X) and isprime(P) then print(X);
end if
end do

Mathematica

Select[Prime@ Range@ 300, PrimeQ[# + Prime[#] + 1] &] (* Giovanni Resta, Aug 16 2018 *)

Prog

(PARI) isok(p) = isprime(p) && isprime(prime(p) + p + 1); \\ Michel Marcus, Aug 16 2018

Crossrefs

Cf. A112885.

Sequence in context: A152533 A228485 A161896 * A304372 A167610 A295149

Adjacent sequences: A317906 A317907 A317908 * A317910 A317911 A317912

Keyword

nonn

Author

David James Sycamore, Aug 10 2018

Status

approved