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Search: id:A114345
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| A114345 |
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Sequence of primes given by the powers of the golden mean function j[n]=n/Log[n]. |
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1
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| 2, 3, 7, 11, 17, 47, 61, 97, 173, 367, 1367, 10631, 13781, 15919, 1008001, 2584403, 4232351, 5459719, 334525987, 11779122851, 13808301271, 116757956759, 2968189088940281, 32797072183910341, 5972846330691787903
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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One of several experiments in generating the primes using power functions of the golden mean
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FORMULA
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g[n]= If[Mod[Floor[Phi^(n/Log[n])], 2] == 0, Floor[Phi^(n/Log[n])], 0] f[n] = f[n - 1] + g[n] a(n) = if PrimeQ[f[n]]==True then f[n]
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MATHEMATICA
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Phi = (1 + Sqrt[5])/2 digits = 1000 g[n_] := If[Mod[Floor[Phi^(n/Log[n])], 2] == 0, Floor[Phi^(n/Log[n])], 0] f[1] = 2; f[2] = 3; f[n_] := f[n] = f[n - 1] + g[n] a = Flatten[Table[f[n], {n, 1, digits}]]; ListPlot[a, PlotJoined -> True] b = Union[Flatten[Table[If[PrimeQ[f[n]] == True, f[n], {}], {n, 1, digits}]]]
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CROSSREFS
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Adjacent sequences: A114342 A114343 A114344 this_sequence A114346 A114347 A114348
Sequence in context: A045325 A094066 A060341 this_sequence A077165 A090666 A140409
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 08 2006
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