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A330067
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Beatty sequence for sinh(x), where 1/x + 1/sinh(x) = 1.
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3
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2, 5, 7, 10, 12, 15, 17, 20, 22, 25, 27, 30, 32, 35, 37, 40, 42, 45, 47, 50, 53, 55, 58, 60, 63, 65, 68, 70, 73, 75, 78, 80, 83, 85, 88, 90, 93, 95, 98, 100, 103, 106, 108, 111, 113, 116, 118, 121, 123, 126, 128, 131, 133, 136, 138, 141, 143, 146, 148, 151
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OFFSET
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1,1
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COMMENTS
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Let x be the solution of 1/x + csch(x) = 1. Then (floor(n x) and (floor(n sinh(x))) are a pair of Beatty sequences; i.e., every positive integer is in exactly one of the sequences. See the Guide to related sequences at A329825.
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LINKS
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FORMULA
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a(n) = floor(n sinh(x)), where x = 1.656135560... is the constant in A330065.
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MATHEMATICA
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r = x /. FindRoot[1/x + 1/Sinh[x] == 1, {x, 2, 10}, WorkingPrecision -> 210]
Table[Floor[n*r], {n, 1, 250}] (* A330066 *)
Table[Floor[n*Sinh[r]], {n, 1, 250}] (* A330067 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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