login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A038626 Smallest positive integer m such that m = pi(n*m) = A000720(n*m). 7
1, 9, 24, 66, 168, 437, 1051, 2614, 6454, 15927, 40071, 100346, 251706, 637197, 1617172, 4124436, 10553399, 27066969, 69709679, 179992838, 465769802, 1208198523, 3140421715, 8179002095, 21338685402, 55762149023, 145935689357, 382465573481, 1003652347080, 2636913002890, 6935812012540 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

Golomb shows that solutions exist for each n>1.

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

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

LINKS

Table of n, a(n) for n=2..32.

S. W. Golomb, On the Ratio of N to pi(N), American Mathematical Monthly, 69 (1962), 36-37.

Eric Weisstein's World of Mathematics, Prime Counting Function.

FORMULA

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

EXAMPLE

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

CROSSREFS

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

Sequence in context: A079770 A079771 A258438 * A195970 A223372 A180334

Adjacent sequences:  A038623 A038624 A038625 * A038627 A038628 A038629

KEYWORD

nonn,changed

AUTHOR

Jud McCranie

EXTENSIONS

a(24) from Farideh Firoozbakht, Jan 09 2005

Edited by N. J. A. Sloane at the suggestion of Chris K. Caldwell, Apr 08 2008

a(25)-a(32) from Max Alekseyev, Jul 18 2011, Oct 14 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified October 22 08:16 EDT 2017. Contains 293758 sequences.