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A330143
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Beatty sequence for (3/2)^x, where (3/2)^x + (5/2)^x = 1.
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3
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1, 3, 4, 6, 7, 9, 10, 12, 14, 15, 17, 18, 20, 21, 23, 25, 26, 28, 29, 31, 32, 34, 36, 37, 39, 40, 42, 43, 45, 47, 48, 50, 51, 53, 54, 56, 58, 59, 61, 62, 64, 65, 67, 68, 70, 72, 73, 75, 76, 78, 79, 81, 83, 84, 86, 87, 89, 90, 92, 94, 95, 97, 98, 100, 101
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OFFSET
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1,2
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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 (3/2)^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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