A038626 - OEIS

%I #44 Oct 13 2023 11:46:58

%S 1,9,24,66,168,437,1051,2614,6454,15927,40071,100346,251706,637197,

%T 1617172,4124436,10553399,27066969,69709679,179992838,465769802,

%U 1208198523,3140421715,8179002095,21338685402,55762149023,145935689357,382465573481,1003652347080,2636913002890,6935812012540

%N Smallest positive integer m such that m = pi(n*m) = A000720(n*m).

%C Golomb shows that solutions exist for each n>1.

%C For all known terms, we have 2.4*a(n) < a(n+1) < 2.7*a(n) + 7. A038627(n) gives number of natural solutions of the equation m = pi(n*m). - _Farideh Firoozbakht_, Jan 09 2005

%C a(n) grows as exp(n)/n. Thus, a(n+1)/a(n) tends to e=exp(1) as n grows. - _Max Alekseyev_, Oct 15 2017

%H Giovanni Resta, <a href="/A038626/b038626.txt">Table of n, a(n) for n = 2..50</a>

%H S. W. Golomb, <a href="http://www.jstor.org/stable/2312732">On the Ratio of N to pi(N)</a>, American Mathematical Monthly, 69 (1962), 36-37.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeCountingFunction.html">Prime Counting Function.</a>

%F a(n) = limit of f^(k)(1) as k grows, where f(x)=A000720(n*x). Also, a(n) = f^(A293529(n))(1). - _Max Alekseyev_, Oct 11 2017

%F a(n) = A038625(n) / n. - _Max Alekseyev_, Oct 13 2023

%e pi(3059) = 437 and 3059/437 = 7, so a(7)=437.

%Y Cf. A038623, A038624, A038625, A038627, A102281, A087237, A293529.

%K nonn

%O 2,2

%A _Jud McCranie_

%E a(24) from _Farideh Firoozbakht_, Jan 09 2005

%E Edited by _N. J. A. Sloane_ at the suggestion of _Chris K. Caldwell_, Apr 08 2008

%E a(25)-a(32) from _Max Alekseyev_, Jul 18 2011, Oct 14 2017

%E a(33)-a(50) obtained from the values of A038625 computed by _Jan Büthe_. - _Giovanni Resta_, Aug 31 2018