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

1,3

Links

Table of n, a(n) for n=1..105.

Formula

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

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

Mathematica

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

Prog

(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, ", "); ); ))

Crossrefs

Cf. A000720.

Sequence in context: A077463 A084556 A084506 * A364800 A157791 A236857

Adjacent sequences: A071575 A071576 A071577 * A071579 A071580 A071581

Keyword

easy,nonn

Author

Benoit Cloitre, May 31 2002

Status

approved