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A092328
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Solutions of x^2 = ceiling(x*r*floor(x/r)) where r=Pi.
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4
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0, 22, 44, 355, 710, 1065, 1420, 1775, 2130, 2485, 2840, 3195, 312689, 1146408, 5419351, 10838702
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OFFSET
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1,2
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COMMENTS
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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
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)
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LINKS
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MATHEMATICA
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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 *)
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PROG
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(PARI) for(x=0, 2000000, if(x^2==ceil(Pi*x*floor(x/Pi)), print1(x, ", ")))
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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