A088987 - OEIS

%I #9 Jan 07 2017 08:38:31

%S 19,23,29,43,47,53,71,73,79,163,167,173,193,197,199,337,347,349,409,

%T 419,421,521,523,541,569,571,577,601,607,613,719,727,733,971,977,983,

%U 1181,1187,1193,1423,1427,1429,1451,1453,1459,1789,1801,1811,2029,2039,2053

%N Triples of primes between two consecutive prime-indexed primes.

%C Conjecture: There cannot be an even number total of primes between two consecutive prime-indexed primes.

%C The conjecture is true except for the first two prime-indexed primes (3 and 5), which have zero primes between them.

%e prime(prime(4)) = 17, prime(prime(5)) = 31. 19,23,29 are the "only" three primes between 17 and 31.

%o (PARI) pipprimes(n,m) = { for(x=1,n, c=0; p1 = prime(prime(x)); p2 = prime(prime(x+1)); forprime(y=p1+2,p2-2,c++); if(c==m, forprime(y=p1+2, p2-2, print1(y","); ); ) ) }

%K nonn

%O 1,1

%A _Cino Hilliard_, Oct 31 2003

%E Edited by _T. D. Noe_, Apr 14 2009