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%I #17 Sep 22 2018 04:24:58
%S 5,109,1913,2081,2351,2897,3169,4027,4397,8221,9461,9661,13613,14969,
%T 17117,17483,24133,28109,31513,32969,47417,60149,61627,73259,84809,
%U 89213,105929,113051,124121,143477,152767,156671,159667,162947,174893,209621,219533,223637,241463,243469,250307,263591
%N Prime-indexed primes q such that prime(q) + q + 1 is a prime-indexed prime.
%C 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.
%H N. Fernandez, <a href="http://www.borve.org/primeness/FOP.html">An order of primeness, F(p)</a>
%H N. Fernandez, <a href="/A006450/a006450.html">An order of primeness</a> [cached copy, included with permission of the author]
%e a(1) is 5 because 5 = prime(3) and prime(5) + 5 + 1 = 17 = prime(7), and no smaller prime has this property.
%p N:=300000:
%p for n from 1 to N do
%p if isprime(n) then q:=ithprime(n);
%p Z:=numtheory[pi](n);
%p P:=q+n+1;
%p R:=numtheory[pi](P);
%p if isprime(Z) and isprime(P) and isprime(R) then print(n);
%p end if:
%p end if:
%p end do:
%o (PARI) isok(p) = isprime(p) && isprime(primepi(p)) && isprime(q=prime(p)+p+1) && isprime(primepi(q)); \\ _Michel Marcus_, Sep 19 2018
%Y Cf. A000040, A006450.
%K nonn
%O 1,1
%A _David James Sycamore_, Aug 22 2018