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A024812
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Numbers n for which there is exactly one positive integer m such that n = floor(cot(Pi/(2m))).
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4
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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
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1,1
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COMMENTS
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LINKS
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FORMULA
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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
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MATHEMATICA
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f[n_] := Floor[Cot[Pi/(2 n)]]; f[ Select[ Range[2, 245], f[# - 1] < f[#] < f[# + 1] &]] (* Robert G. Wilson v, Mar 27 2013 *)
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PROG
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(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]
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CROSSREFS
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A024813 yields the corresponding values of m.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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