A024812 - OEIS

A024812

Numbers n for which there is exactly one positive integer m such that n = floor(cot(Pi/(2m))).

2, 4, 7, 9, 11, 14, 16, 18, 21, 23, 25, 28, 30, 32, 34, 37, 39, 41, 44, 46, 48, 51, 53, 55, 58, 60, 62, 65, 67, 69, 72, 74, 76, 79, 81, 83, 86, 88, 90, 93, 95, 97, 100, 102, 104, 107, 109, 111, 114, 116, 118, 121, 123, 125, 128, 130, 132, 135, 137, 139, 142, 144, 146, 149, 151, 153

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OFFSET

1,1

COMMENTS

Conjecture (verified for k <= 10^6 by M. F. Hasler): A024812(k) = (A024813(k)+k-1)/2, k=1,2,.... - L. Edson Jeffery, Mar 21 2013

LINKS

Table of n, a(n) for n=1..66.

FORMULA

a(k) = floor(cot(Pi/(2*A024813(k)))). - L. Edson Jeffery, Mar 21 2013

Conjecture: a(n) = a(n-1) + a(n-3) - a(n-4); g.f.: x*(x^15-x^14+3*x^2+2*x+2) / ((x-1)^2*(x^2+x+1)). - Colin Barker, Jan 03 2014

MATHEMATICA

f[n_] := Floor[Cot[Pi/(2 n)]]; f[ Select[ Range[2, 245], f[# - 1] < f[#] < f[# + 1] &]] (* Robert G. Wilson v, Mar 27 2013 *)

PROG

(PARI) {my(f(m)=floor(cotan(Pi/(2*m)))); for(m=2, 999, f(m-1)<f(m) & f(m)<f(m+1) & print1(f(m)", "))} \\ Note: Depending on default(realprecision), e.g. when this is set to 99, floor(cotan(Pi/4)) may yield 0 and erroneous output of f(3)=1. [M. F. Hasler, Mar 20 2013]

CROSSREFS

A024813 yields the corresponding values of m.

Sequence in context: A160822 A111495 A187686 * A047349 A329842 A054406

Adjacent sequences: A024809 A024810 A024811 * A024813 A024814 A024815

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

Definition corrected, following posts to the SeqFan list from Harvey P. Dale and Don Reble, by M. F. Hasler, Mar 20 2013

STATUS

approved