

A091987


Number of steps required for initial p = 2^n to reach 0 in the recurrence p = pi(p).


0



1, 2, 3, 4, 5, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 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
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OFFSET

0,2


LINKS

Table of n, a(n) for n=0..64.
Andrew Booker, The Nth Prime Page.


FORMULA

pi(n) = A000720(n) = number of primes less than or equal to n. By repeating n=pi(n), n will reach 0 in a finite number of steps.


EXAMPLE

Pi(32) = 11
Pi(11) = 5
Pi(5) = 3
Pi(3) = 2
Pi(2) = 1
Pi(1) = 0
Total steps to reach 0 = 6. Thus 6 is the 6th entry in the sequence corresponding to n=5.


MATHEMATICA

Table[Length[NestWhileList[PrimePi, 2^n, #>0&]]1, {n, 0, 40}] (* Harvey P. Dale, May 29 2016 *)


PROG

(PARI) pr2n(n) = my(c); for(x=0, n, y=2^x; c=0; p=y; while(p, p = primepi(p); c++); print1(c", "))


CROSSREFS

Cf. A000720.
Sequence in context: A097622 A236561 A110010 * A025544 A327706 A121856
Adjacent sequences: A091984 A091985 A091986 * A091988 A091989 A091990


KEYWORD

hard,nonn


AUTHOR

Cino Hilliard, Mar 16 2004


EXTENSIONS

More terms from Harvey P. Dale, May 29 2016
a(41)a(64) from Chai Wah Wu, May 25 2018


STATUS

approved



