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A076936
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a(1) = 1; then the smallest number different from its predecessor such that the n-th partial product is an n-th power.
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2
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1, 4, 2, 32, 4, 256, 8, 2048, 16, 16384, 32, 131072, 64, 1048576, 128, 8388608, 256, 67108864, 512, 536870912, 1024, 4294967296, 2048, 34359738368, 4096, 274877906944, 8192, 2199023255552, 16384, 17592186044416, 32768
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OFFSET
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1,2
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COMMENTS
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Or "such that the geometric mean of the first n terms is an integer." (Without the "different from its predecessor" requirement, the trivial sequence 1,4,2,2,2,2,2,... would have resulted.)
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LINKS
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FORMULA
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G.f.: x*(1+4*x-8*x^2-8*x^3)/(1-10*x^2+16*x^4). (End)
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MAPLE
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MATHEMATICA
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CoefficientList[Series[x (1 + 4 x - 8 x^2 - 8 x^3)/(1 - 10 x^2 + 16 x^4), {x, 0, 31}], x] (* Michael De Vlieger, Nov 24 2017 *)
LinearRecurrence[{0, 10, 0, -16}, {1, 4, 2, 32}, 40] (* Harvey P. Dale, Mar 20 2024 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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