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

0,1

Comments

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

Links

Table of n, a(n) for n=0..72.

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A287643 A114955 A209384 * A195932 A327707 A134679

Adjacent sequences: A060204 A060205 A060206 * A060208 A060209 A060210

Keyword

nonn

Author

Labos Elemer, Mar 19 2001

Extensions

More terms from David Wasserman, May 31 2002

Status

approved