

A091988


Number of steps required for initial p = 2^n to reach 1 in the recurrence p = floor(Li(p)).


0



1, 2, 4, 5, 5, 6, 6, 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, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 22, 22
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OFFSET

1,2


COMMENTS

Except for the first few terms, corresponding terms in this sequence and the one using pi(n) are equal. If we define Li(1) = 0 then the terms will differ by 1 since we carry the pi(n) calculation to pi(1) which is 0.


LINKS

Table of n, a(n) for n=1..74.
Andrew Booker, The Nth Prime Page.


FORMULA

Li(n) = logarithmic integral Li(x) = integral(x=2..n, dx/log(x)) ~ pi(n) = number of primes less than or equal to n. Repeating n = Li(n), n will reach 1 in a finite number of steps.


PROG

(PARI) Li(x) = eint1(log(x))
pr2nLi(n) = my(c); for(x=1, n, y=2^x; c=0; p=y; while(p > 1, p = floor(Li(p)); c++); print(x" "c", "))


CROSSREFS

Sequence in context: A083038 A061008 A256720 * A023824 A341744 A081252
Adjacent sequences: A091985 A091986 A091987 * A091989 A091990 A091991


KEYWORD

easy,nonn


AUTHOR

Cino Hilliard, Mar 16 2004


STATUS

approved



