A072677 a(n) = prime(prime(n)+1) where prime(k) is the k-th prime.

5, 7, 13, 19, 37, 43, 61, 71, 89, 113, 131, 163, 181, 193, 223, 251, 281, 293, 337, 359, 373, 409, 433, 463, 521, 557, 569, 593, 601, 619, 719, 743, 787, 809, 863, 881, 929, 971, 997, 1033, 1069, 1091, 1163, 1181, 1213, 1223, 1301, 1423, 1439, 1451, 1481, 1511, 1531, 1601, 1627, 1693, 1733, 1747, 1789, 1831, 1861, 1931

Offset: 1

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Jul 05 2002

Keywords

• easy
• nonn

Comments

Prime numbers q for which the number of prime numbers smaller than q is also a prime number.

Examples

			a(4)=prime(prime(4)+1), prime(4)=7, hence a(4)=prime(8)=19.
163 is in the sequence because (1) it is a prime number, (2) there are 37 prime numbers smaller than 163 and 37 is also a prime number.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000720, A006450, A055003, A072677.

Programs

Maple

with(numtheory): seq(ithprime(ithprime(i)+1),i=1..51);

Mathematica

Prime[Prime[Range[60]]+1] (* Harvey P. Dale, Nov 07 2016 *)

PARI

a(n) = prime(prime(n)+1); \\ Michel Marcus, Nov 17 2017

Extensions

Edited by N. J. A. Sloane, Nov 04 2018 at the suggestion of Georg Fischer, Nov 03 2018, merging a duplicate entry with this one.