A062300 a(n) = floor(cosec(Pi/(n+1))).

1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 19, 19, 19, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 23, 23, 23, 24, 24, 24, 25, 25

Offset: 1

Author

Amarnath Murthy, Jun 19 2001

Keywords

• nonn
• easy

Comments

cosec = 1/sin. - Kevin Ryde observes that this sequences is up to the offset almost identical to A032615(n) = floor(n/Pi): the values differ after n=6 for the first time again at n=80143857. Robert Israel shows that we can nonetheless expect infinitely many differences. See the posts on the SeqFan list for details. - M. F. Hasler, Oct 19 2016

Examples

			a(99) = 31 as cosec{Pi/100} =31.8362252090976229556628738787913...
		

Links

• Harry J. Smith, Table of n, a(n) for n=1..1000
• R. Israel, in reply to K. Ryde, Re: nearly equal floor(n/Pi) A032615 and A062300, SeqFan list, Oct 19 2016

Crossrefs

Cf. A032615.

Programs

PARI

v=vector(150,n,floor(1/sin(Pi/(n+1)))) \\ Warning: for n=5 this may yield an incorrect value of 1 instead of a(n)=2, depending on default(realprecision).

PARI

{ default(realprecision, 50); for (n=1, 1000, write("b062300.txt", n, " ", floor(1/sin(Pi/(n+1)))) ) } \\ Harry J. Smith, Aug 04 2009

PARI

A062300(n,e=.1^precision(.1))=1\sin(Pi/(n+1+e)) \\ M. F. Hasler, Oct 19 2016

Extensions

More terms from Jason Earls, Jun 22 2001