OFFSET
1,1
COMMENTS
Conjecture: For x > 1 there is at least 1 prime between prime(prime(x)) and prime(prime(x+1)).
This conjecture is equivalent to saying that there is at least one prime index between prime(x) and prime(x+1), which is trivially true because both are odd for x > 1; one has prime(prime(x)) < prime(prime(x)+1) < prime(prime(x+1)). Obviously the definition is equivalent to "primes > 2 with nonprime index", i.e., sequence A007821 without the initial 2. - M. F. Hasler, Jul 31 2015
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..5000
FORMULA
Primes p such that prime(prime(x)) < p < prime(prime(x+1)).
EXAMPLE
Prime(prime(4)) = 17 and prime(prime(5)) = 31 and 19,23,29 are between 17 and 31, so 19, 23 and 29 are members.
MATHEMATICA
Flatten[Table[Prime[Range[Prime[n]+1, Prime[n+1]-1]], {n, 30}]] (* Harvey P. Dale, Mar 22 2015 *)
PROG
(PARI) pipprimes(n) = { for(x=1, n, c=-2; p1 = prime(prime(x)); p2 = prime(prime(x+1)); forprime(y=p1, p2, c++; if(y > p1 && y < p2, print1(y", ")); ); ) }
(PARI) forcomposite(n=2, 100, print1(prime(n)", ")) \\ M. F. Hasler, Jul 31 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Cino Hilliard, Oct 31 2003
STATUS
approved