A318752 Prime-indexed primes q such that prime(q) + q + 1 and prime(q) - q - 1 are both prime-indexed primes.

5, 486509, 1545959, 5516507, 10673177, 11843309, 14773877, 22201349, 40600349, 43228709, 44489657, 60376133, 76232459, 83005829, 94265687, 125445101, 164054921, 165553511, 176691533, 199379657, 208672097, 228757709, 238916543, 240583781, 243132233, 243211679, 243443303, 243564509, 260234813

Offset

1,1

Comments

Intersection of A318292 and A318751, subsequence of A006450.

Links

Daniel Suteu, Table of n, a(n) for n = 1..100

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

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

Daniel Suteu, Perl program

Example

Prime(3) = 5 is in the sequence: it is a prime-indexed prime, prime(5) + 5 + 1 = 11 + 5 + 1 = 17 = prime(7) is a prime-indexed prime, and prime(5) - 5 - 1 = 5 = prime(3) is also a prime-indexed prime.

Maple

N := 25000000:
for n to N do
if isprime(n) then q := ithprime(n);
Z := numtheory[pi](n);
P := q+n+1;
S := q-n-1;
X := numtheory[pi](P);
W := numtheory[pi](S);
if isprime(Z) and isprime(P) and isprime(S) and isprime(X) and isprime(W) 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)) && isprime(qq=prime(p)+p+1) && isprime(primepi(qq)); \\ Michel Marcus, Sep 03 2018

Crossrefs

Cf. A000040, A006450, A318292, A318751.

Sequence in context: A240132 A067509 A067502 * A123693 A269527 A111727

Adjacent sequences: A318749 A318750 A318751 * A318753 A318754 A318755

Keyword

nonn

Author

David James Sycamore, Sep 02 2018

Extensions

a(13)-a(29) from Daniel Suteu, Nov 11 2018

Status

approved