A120701 - OEIS

%I #25 Aug 26 2023 02:52:58

%S 2,6,9,12,15,18,21,25,28,31,34,37,40,43,47,50,53,56,59,62,65,69,72,75,

%T 78,81,84,87,91,94,97,100,103,106,109,113,116,119,122,125,128,131,135,

%U 138,141,144,147,150,153,157,160,163,166,169,172,175,179,182,185,188

%N Number of unit circles which fit touching a circle of radius n-1, i.e., with their centers on a circle of radius n.

%C Coincides with A022844 = floor(n*Pi) except at n=1, 25510582, ... (sequence A120702).

%H G. C. Greubel, <a href="/A120701/b120701.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = floor(Pi/arcsin(1/n)).

%t Table[Floor[Pi/ArcSin[1/n]], {n, 60}] (* _Indranil Ghosh_, Jul 21 2017 *)

%o (Python)

%o from mpmath import mp, pi, asin

%o mp.dps=100

%o def a(n): return int(floor(pi/asin(1./n)))

%o print([a(n) for n in range(1, 61)]) # _Indranil Ghosh_, Jul 21 2017

%o (SageMath) [floor(pi/arcsin(1/n)) for n in range(1,71)] # _G. C. Greubel_, Aug 25 2023

%o (Magma) R:= RealField(30); [Floor(Pi(R)/Arcsin(1/n)) : n in [1..70]]; // _G. C. Greubel_, Aug 25 2023

%Y Cf. A001116, A002486, A022844, A120702.

%K easy,nonn

%O 1,1

%A _Martin Fuller_, Jun 28 2006