A077510 Numbers k such that k + pi(k) is a prime.

2, 3, 7, 9, 12, 13, 21, 28, 32, 36, 45, 52, 55, 57, 61, 65, 70, 76, 79, 81, 84, 86, 89, 101, 104, 110, 119, 121, 131, 135, 139, 145, 147, 155, 160, 162, 172, 181, 185, 187, 195, 205, 216, 222, 223, 228, 231, 253, 258, 262, 273, 278, 286, 288, 292, 297, 305, 310

Offset: 1

Author

Amarnath Murthy, Nov 08 2002

Keywords

• nonn

Comments

Conjecture: for k > 5, prime(n) <= k < prime(n+1) <= k + pi(k), i.e., the smallest prime greater than k is <= k + pi(k). Equality holds for k = 7.

Examples

			21 is a member as 21 + pi(21) = 21 + 8 = 29 is a prime.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A000720, A061067, A076757.

Programs

Mathematica

Select[Range[350],PrimeQ[#+PrimePi[#]]&] (* Harvey P. Dale, Nov 19 2011 *)

PARI

for(n=1,200,if(isprime(n+primepi(n)),print1(n,", "))) \\ Derek Orr, Jun 22 2015

PARI

pi=0; p=2; forprime(q=3,1e3, pi++; for(n=p,q-1, if(isprime(n+pi), print1(n", "))); p=q) \\ Charles R Greathouse IV, Jun 23 2015

Extensions

More terms from David Garber, Nov 10 2002