A156152 Primes p such that p = 2 (mod pi(p)), where pi(p) = A000720(p) is the prime counting function.

2, 5, 41, 47, 347, 367, 9559817, 514272793, 514274807, 514275529, 3779851091, 27788568469, 27788573621, 204475055227, 11091501631937, 81744303098923, 602656752070661, 602656752071189, 241849345578327359, 241849345578328451, 241849345578337811, 1784546064357416683

Offset: 1

Author

M. F. Hasler, Feb 04 2009

Keywords

• nonn

Links

• Giovanni Resta, Table of n, a(n) for n = 1..28

Crossrefs

Cf. A156151, A156153 (primes from this sequence).

Programs

Mathematica

f[p_,n_]:=Mod[p,n]==2; lst={};Do[p=Prime[n];If[f[p,n],AppendTo[lst,p]],{n,11!}];lst (* Vladimir Joseph Stephan Orlovsky, Dec 08 2009 *)

PARI

p=c=0; until(0, (-2+p=nextprime(p+1))%c++ || print1(p, ", "))

Formula

a(n) = A000040(A023144(n)).

Extensions

More terms from Max Alekseyev, May 03 2009

a(15)-a(16) from Jinyuan Wang, Feb 22 2020

Terms a(17) and beyond from Giovanni Resta, Feb 23 2020