A092328 Solutions of x^2 = ceiling(x*r*floor(x/r)) where r=Pi.

0, 22, 44, 355, 710, 1065, 1420, 1775, 2130, 2485, 2840, 3195, 312689, 1146408, 5419351, 10838702

Offset: 1

Author

Benoit Cloitre, Feb 14 2004

Keywords

• nonn
• more

Comments

Does limit n->infinity log(a(n))/n exist?

Notice that the entries above are either numerators of convergents to Pi (A002485) or multiples thereof. - Robert G. Wilson v, Feb 26 2004

a(23) <= 430010946591069243. - Robert G. Wilson v, Jul 19 2019

From M. F. Hasler, Sep 10 2020: (Start)

Appears to be the same as: n >= 0 such that n*tan(n) < 1, cf. A332095. Is there a counterexample?

Most terms are multiples of a smaller term: 44 = 22*2 and a(4..12) = {355, 710, 1065, 1420, 1775, 2130, 2485, 2840, 3195} = 355*{1, 2, 3, ..., 9}. See A332095 for more. (End)

Crossrefs

Cf. A249836, A088306, A332095.

Programs

Mathematica

Do[ If[ n^2 == Ceiling[n*3.1415926535897932346264*Floor[n/3.1415926535897932346264]], Print[n]], {n, 0, 10^8}] (* Robert G. Wilson v, Feb 26 2004 *)

PARI

for(x=0,2000000,if(x^2==ceil(Pi*x*floor(x/Pi)),print1(x,",")))

Extensions

More terms from Robert G. Wilson v, Feb 26 2004