A088982 Primes that are between consecutive prime-indexed primes.

7, 13, 19, 23, 29, 37, 43, 47, 53, 61, 71, 73, 79, 89, 97, 101, 103, 107, 113, 131, 137, 139, 149, 151, 163, 167, 173, 181, 193, 197, 199, 223, 227, 229, 233, 239, 251, 257, 263, 269, 271, 281, 293, 307, 311, 313, 317, 337, 347, 349, 359, 373, 379, 383, 389

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)).

a(n) = prime(composite(n)) = A000040(A002808(n)). - Terry D. Grant, Aug 16 2016

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 *)
Table[Prime[Composite(n)] , {n, 1, 100}]  (* Terry D. Grant, Aug 16 2016 *)

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

Essentially the same as A007821.

Sequence in context: A371166 A340105 A309649 * A354460 A176406 A033561

Adjacent sequences: A088979 A088980 A088981 * A088983 A088984 A088985

Keyword

nonn

Author

Cino Hilliard, Oct 31 2003

Status

approved