A091988 Number of steps required for initial p = 2^n to reach 1 in the recurrence p = floor(Li(p)).

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

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