login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A088982 Primes that are between consecutive prime-indexed primes. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A320629 A340105 A309649 * A176406 A033561 A227030

Adjacent sequences:  A088979 A088980 A088981 * A088983 A088984 A088985

KEYWORD

nonn

AUTHOR

Cino Hilliard, Oct 31 2003

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 23 19:26 EDT 2021. Contains 348215 sequences. (Running on oeis4.)