A072677 - OEIS

%I #12 Nov 04 2018 13:35:10

%S 5,7,13,19,37,43,61,71,89,113,131,163,181,193,223,251,281,293,337,359,

%T 373,409,433,463,521,557,569,593,601,619,719,743,787,809,863,881,929,

%U 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

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

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

%H Alois P. Heinz, <a href="/A072677/b072677.txt">Table of n, a(n) for n = 1..10000</a>

%e a(4)=prime(prime(4)+1), prime(4)=7, hence a(4)=prime(8)=19.

%e 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.

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

%t Prime[Prime[Range[60]]+1] (* _Harvey P. Dale_, Nov 07 2016 *)

%o (PARI) a(n) = prime(prime(n)+1); \\ _Michel Marcus_, Nov 17 2017

%Y Cf. A000720, A006450, A055003, A072677.

%K easy,nonn

%O 1,1

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

%E 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.