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%I #13 Mar 04 2024 11:02:06
%S 2,3,7,9,12,13,21,28,32,36,45,52,55,57,61,65,70,76,79,81,84,86,89,101,
%T 104,110,119,121,131,135,139,145,147,155,160,162,172,181,185,187,195,
%U 205,216,222,223,228,231,253,258,262,273,278,286,288,292,297,305,310
%N Numbers n such that n + pi(n) is a prime.
%C 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.
%H Charles R Greathouse IV, <a href="/A077510/b077510.txt">Table of n, a(n) for n = 1..10000</a>
%e 21 is a member as 21 + pi(21) = 21 + 8 = 29 is a prime.
%t Select[Range[350],PrimeQ[#+PrimePi[#]]&] (* _Harvey P. Dale_, Nov 19 2011 *)
%o (PARI) for(n=1,200,if(isprime(n+primepi(n)),print1(n,", "))) \\ _Derek Orr_, Jun 22 2015
%o (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
%Y Cf. A000040, A000720, A061067, A076757.
%K nonn
%O 1,1
%A _Amarnath Murthy_, Nov 08 2002
%E More terms from _David Garber_, Nov 10 2002
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