A088985 Numbers of the form prime(prime(n)+1), with n satisfying prime(n)+2 = prime(n+1).

7, 13, 37, 61, 113, 181, 281, 359, 557, 593, 787, 863, 1069, 1163, 1213, 1439, 1511, 1733, 1831, 2069, 2347, 2903, 3011, 3271, 3739, 4139, 4409, 4561, 4783, 4937, 6221, 6317, 6359, 6659, 6857, 8111, 8231, 8387, 8521, 8753, 9311, 10007, 10453

Offset

1,1

Comments

Also, prime numbers p such that there exists a positive integer n with the property that p is the only prime satisfying prime(prime(n)) < p < prime(prime(n+1)).

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

prime(3) + 2 = prime(4), hence prime(prime(3)+1) = 13 is in the sequence.

Mathematica

a={}; For[n=1, n<210, n++, If[Prime[n+1]==Prime[n]+2, AppendTo[a, Prime[Prime[n]+1]]]]; a
Prime[#+1]&/@Select[Partition[Prime[Range[300]], 2, 1], #[[2]]-#[[1]] == 2&][[All, 1]] (* Harvey P. Dale, Feb 27 2021 *)

Prog

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

Crossrefs

Sequence in context: A173230 A361483 A155036 * A022005 A281317 A336773

Adjacent sequences: A088982 A088983 A088984 * A088986 A088987 A088988

Keyword

nonn

Author

Cino Hilliard, Oct 31 2003

Extensions

Edited by Stefan Steinerberger, Jul 27 2007

Status

approved