

A077510


Numbers n such that n + pi(n) is a prime.


5



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
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OFFSET

1,1


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.


LINKS

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


EXAMPLE

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


MATHEMATICA

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


PROG

(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, q1, if(isprime(n+pi), print1(n", "))); p=q) \\ Charles R Greathouse IV, Jun 23 2015


CROSSREFS

Cf. A061067, A076757.
Sequence in context: A262814 A328982 A260641 * A178433 A073148 A014839
Adjacent sequences: A077507 A077508 A077509 * A077511 A077512 A077513


KEYWORD

nonn


AUTHOR

Amarnath Murthy, Nov 08 2002


EXTENSIONS

More terms from David Garber, Nov 10 2002


STATUS

approved



