A304372 Primes p such that prime(p) + p + 1 and prime(p) - p - 1 are both prime.

5, 11, 23, 29, 149, 269, 293, 347, 617, 647, 683, 761, 809, 1259, 1553, 1619, 2003, 2063, 2081, 2129, 2297, 2309, 2381, 2579, 2693, 2897, 3023, 3557, 4241, 4721, 4799, 4817, 5519, 6197, 6719, 6833, 6959, 8237, 8537, 8597, 8783, 9029, 9461, 9677, 9929

Offset

1,1

Comments

Subsequence of A317909 and consequently the resulting primes are a subsequence of A112885 (see A317909 for proof).

Links

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

Example

p=5; prime(5) + 5 + 1 = 17 and prime(5) - 5 - 1 = 5, both prime so 5 is a member, and since the same does not hold for primes 2 and 3, a(1)=5.

Maple

N:=5000:
for X from 1 to N do
A:=ithprime(X);
P:=A+X+1;
Q:=A-X-1;
if isprime(X) and isprime(P) and isprime(Q) then print(X);
end if:
end do:

Mathematica

Select[Prime[Range[2 10^3]], And@@PrimeQ[{Prime[#] + # + 1, Prime[#] - # - 1}] &] (* Vincenzo Librandi, Aug 18 2018 *)

Prog

(Magma) [n: n in [1..2*10^4] | IsPrime(n) and IsPrime (NthPrime(n)+n+1) and IsPrime (NthPrime(n)-n-1)]; // Vincenzo Librandi, Aug 18 2018
(PARI) isok(p) = isprime(p) && isprime(prime(p) + p + 1) && isprime(prime(p) - p - 1); \\ Michel Marcus, Aug 18 2018

Crossrefs

Cf. A112885, A317909.

Sequence in context: A228485 A161896 A317909 * A167610 A295149 A143127

Adjacent sequences: A304369 A304370 A304371 * A304373 A304374 A304375

Keyword

nonn,easy

Author

David James Sycamore, Aug 16 2018

Extensions

More terms from Vincenzo Librandi, Aug 18 2018

Status

approved