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A079372
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Costé prime expansion of sqrt(2) - 1.
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3
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3, 5, 5, 17, 11, 3, 29, 31, 29, 13, 7, 37, 7, 5, 3, 5, 5, 5, 11, 17, 7, 13, 13, 17, 11, 5, 3, 31, 31, 53, 41, 97, 47, 19, 17, 17, 41, 71, 29, 11, 211, 23, 79, 17, 5, 7, 23, 17, 5, 3, 11, 5, 2, 17, 7, 17, 5, 2, 23, 11, 3, 3, 5, 5, 3, 3, 5
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OFFSET
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0,1
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COMMENTS
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For x in (0,1], define P(x) = min{p: p prime, 1/x < p}, Phi(x) = P(x)x - 1. Costé prime expansion of x(0) is sequence a(0), a(1), ... given by x(n) = Phi(x(n-1)) (n>0), a(n) = P(x(n)) (n >= 0).
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LINKS
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MAPLE
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Digits := 200: P := proc(x) local y; y := ceil(evalf(1/x)); if isprime(y) then y else nextprime(y); fi; end; F := proc(x) local y, i, t1; y := x; t1 := []; for i from 1 to 50 do p := P(y); t1 := [op(t1), p]; y := p*y-1; od; t1; end; F(sqrt(2)-1);
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MATHEMATICA
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$MaxExtraPrecision = 500; P[x_] := Module[{y}, y = Ceiling[1/x]; If[PrimeQ[y], y, NextPrime[y]]]; F[x_] := Module[{y, i, t1}, y = x; t1 = {}; For[i = 1, i <= 100, i++, AppendTo[t1, p = P[y]]; y = p*y - 1]; t1]; F[Sqrt[2] -1] (* G. C. Greubel, Jan 20 2019 *)
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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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