A071578 Number of iterations of Pi(n) needed to reach 1, where Pi(x) denotes the number of primes <= x.

0, 1, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

Offset: 1

Author

Benoit Cloitre, May 31 2002

Keywords

• easy
• nonn

Crossrefs

Cf. A000720.

Programs

Mathematica

Table[Length[NestWhileList[PrimePi[#]&,n,#!=1&]]-1,{n,110}] (* Harvey P. Dale, Dec 24 2018 *)

PARI

for(n=2,150,s=n; t=0; while(s!=1,t++; s=sum(i=2,s,isprime(i)); if(s==1,print1(t,","); ); ))

Formula

a(n) = a(Pi(n))+1.

a(n) = A060197(n) - 2. - Filip Zaludek, Dec 10 2016