

A060207


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


2



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
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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), 523527.


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



