A060207 Start at 2^n, iterate function PrimePi (A000720) until fixed point is reached; sequence gives number of steps.

2, 3, 4, 5, 6, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22

Offset: 0

Author

Labos Elemer, Mar 19 2001

Keywords

• nonn

Comments

A007097(a(n) - 2) <= 2^n < A007097(a(n) - 1). - David Wasserman, May 31 2002

Examples

			n=24, the relevant list is: {16777216,1077871,84115,8198,1028,172,39,12,5,3,2,1,0}, its length a(24)=13.
		

Links

• S. Segal, On pi(x+y)<=pi(x)+pi(y), Transactions American Mathematical Society, 104 (1962), 523-527.

Crossrefs

Cf. A060208, A007097, A000720, A033844, A071682.

Programs

Mathematica

Table[Length[FixedPointList[PrimePi, 2^w]]-1, {w, 0, 32}]
f[n_] := Length@ NestWhileList[ PrimePi, 2^n, # > 0 &]; Array[f, 48, 0] (* Robert G. Wilson v, Aug 12 2011 *)

PARI

a(n) = {my(c=2, k=2^n); while(k=primepi(k), c++); c; } \\ Jinyuan Wang, May 16 2020

Extensions

More terms from David Wasserman, May 31 2002