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A088306
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Integers n with tan n > |n|, ordered by |n|.
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8
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1, -2, -11, -33, -52174, 260515, -573204, 37362253, -42781604, 122925461, 534483448, 3083975227, 902209779836, -2685575996367, -65398140378926, 74357078147863, 214112296674652, 642336890023956, -5920787228742393, -12055686754159438, 18190586279576483, -48436859313312404
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OFFSET
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1,2
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COMMENTS
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Name was "Positive integers n with |tan n| > n." before signs were added. The sign here shows whether tan(|n|) is positive or negative.
That this sequence is infinite was proved by Bellamy, Lagarias and Lazebnik. It seems not to be known whether there are infinitely many n with tan n > n.
At approximately 2.37e154, there is a value of n which has tan(n)/n > 556. - Phil Carmody, Mar 04 2007 [This is index 214 in the b-file.]
As n increases, log(|a(n)|)/n seems to approach Pi/2; this is similar to what would be expected if an integer sequence were created by drawing many random numbers independently from a uniform distribution on the interval [-Pi/2,+Pi/2] and including in the sequence only those integers j for which the j-th random number x_j happened to satisfy |x_j| < 1/j (and applying to j the sign of x_j). - Jon E. Schoenfield, Aug 19 2014; updated Nov 07 2014 to reflect the change in the sequence's Name)
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LINKS
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MAPLE
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a:=proc(n) if abs(evalf(tan(n)))>n then n else fi end: seq(a(n), n=1..100000); # Emeric Deutsch, Dec 18 2004
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MATHEMATICA
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Select[Range[600000], Abs[Tan[#]]>#&] (* Harvey P. Dale, Nov 30 2012 *)
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PROG
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CROSSREFS
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Cf. A249836 (subsequence of positive terms).
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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