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A318752
Prime-indexed primes q such that prime(q) + q + 1 and prime(q) - q - 1 are both prime-indexed primes.
2
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
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(13)-a(29) from Daniel Suteu, Nov 11 2018
STATUS
approved