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A330144
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Beatty sequence for (5/2)^x, where (3/2)^x + (5/2)^x = 1.
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3
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2, 5, 8, 11, 13, 16, 19, 22, 24, 27, 30, 33, 35, 38, 41, 44, 46, 49, 52, 55, 57, 60, 63, 66, 69, 71, 74, 77, 80, 82, 85, 88, 91, 93, 96, 99, 102, 104, 107, 110, 113, 115, 118, 121, 124, 127, 129, 132, 135, 138, 140, 143, 146, 149, 151, 154, 157, 160, 162
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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 (2/3)^x + (2/5)^x = 1. Then (floor(n*(3/2)^x)) and (floor(n*(5/2)^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 (5/2)^x)), where x = 1.108702608375893... is the constant in A330142.
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MATHEMATICA
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r = x /.FindRoot[(2/3)^x + (2/5)^x == 1, {x, 1, 2}, WorkingPrecision -> 200]
Table[Floor[n*(3/2)^r], {n, 1, 250}] (* A330143 *)
Table[Floor[n*(5/2)^r], {n, 1, 250}] (* A330144 *)
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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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