A318292 Prime-indexed primes q such that prime(q) + q + 1 is a prime-indexed prime.

5, 109, 1913, 2081, 2351, 2897, 3169, 4027, 4397, 8221, 9461, 9661, 13613, 14969, 17117, 17483, 24133, 28109, 31513, 32969, 47417, 60149, 61627, 73259, 84809, 89213, 105929, 113051, 124121, 143477, 152767, 156671, 159667, 162947, 174893, 209621, 219533, 223637, 241463, 243469, 250307, 263591

Offset

1,1

Comments

This sequence and the sequence of resulting primes prime(q)+q+1 (17,709, 18433, 20231, 23251, 29269, 32323, 42181, ...) are subsequences of A006450, the prime indexed primes.

Links

Table of n, a(n) for n=1..42.

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

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

Example

a(1) is 5 because 5 = prime(3) and prime(5) + 5 + 1 = 17 = prime(7), and no smaller prime has this property.

Maple

N:=300000:
for n from 1 to N do
if isprime(n) then q:=ithprime(n);
Z:=numtheory[pi](n);
P:=q+n+1;
R:=numtheory[pi](P);
if isprime(Z) and isprime(P) and isprime(R) then print(n);
end if:
end if:
end do:

Prog

(PARI) isok(p) = isprime(p) && isprime(primepi(p)) && isprime(q=prime(p)+p+1) && isprime(primepi(q)); \\ Michel Marcus, Sep 19 2018

Crossrefs

Cf. A000040, A006450.

Sequence in context: A195561 A142510 A195552 * A012239 A012121 A371882

Adjacent sequences: A318289 A318290 A318291 * A318293 A318294 A318295

Keyword

nonn

Author

David James Sycamore, Aug 22 2018

Status

approved