A318294 Prime-indexed primes p such that 2*p + 1 is also a prime-indexed prime.

5, 41, 1031, 3299, 3761, 6323, 7649, 7841, 10589, 12959, 18443, 37853, 38039, 44729, 58511, 59723, 60509, 77813, 105971, 134489, 137999, 190523, 194933, 200351, 239633, 250751, 266093, 288653, 315011, 366161, 376241, 377633, 393401, 410999, 420419, 420779, 450431, 474983

Offset

1,1

Comments

Prime-indexed Sophie Germain primes whose associated safe primes are also prime-indexed. Subsequence of A005384.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..300

N. Fernandez, An order of primeness, F(p)

N. Fernandez, An order of primeness [cached copy, included with permission of the author]

Example

5 = prime(3) is a prime-indexed prime, and 2*5 + 1 = 11 = prime(5) is also a prime-indexed prime. Therefore 5 is in the sequence.
3 = prime(2) is a prime-indexed prime, but 2*3 + 1 = 7 = prime(4) is not a prime-indexed prime since 4 is composite. Therefore 3 is not in the sequence.

Mathematica

Select[Table[Prime[p], {p, Prime[Range[5000]]}], AllTrue[{2#+1, PrimePi[2#+1]}, PrimeQ]&] (* Harvey P. Dale, Jun 18 2023 *)

Prog

(PARI) isok(p) = isprime(p) && isprime(primepi(p)) && isprime(2*p+1) && isprime(primepi(2*p+1)); \\ Michel Marcus, Aug 28 2018

Crossrefs

Cf. A005384, A006450.

Sequence in context: A342439 A197173 A052113 * A065035 A340535 A145008

Adjacent sequences: A318291 A318292 A318293 * A318295 A318296 A318297

Keyword

nonn

Author

David James Sycamore, Aug 23 2018

Extensions

More terms from Michel Marcus, Aug 28 2018

Status

approved