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A079384 Costé prime expansion of 2^(1/3) - 1. 3
5, 5, 3, 3, 3, 3, 3, 53, 13, 29, 7, 5, 11, 3, 7, 5, 11, 5, 7, 5, 71, 67, 17, 11, 5, 5, 37, 11, 2, 11, 11, 3, 11, 5, 5, 11, 7, 11, 3, 3, 3, 3, 3, 3, 11, 7, 7, 7, 5, 23, 17, 7, 17, 13, 41, 53, 23, 7, 7, 5, 5, 5, 5, 2, 7, 3, 53, 11, 3, 7, 5, 2, 7, 17, 17, 379, 107, 41, 19, 11, 5, 5, 2, 5, 5, 3, 11, 2, 29, 11, 7, 7, 13, 29, 7, 53, 53, 17, 11, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..2000

A. Costé, Sur un système fibré lié à la suite des nombres premiers, Exper. Math., 11 (2002), 383-405.

MAPLE

Digits := 500: 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 100 do p := P(y); t1 := [op(t1), p]; y := p*y-1; od; t1; end; F(2^(1/3) - 1);

MATHEMATICA

$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[Surd[2, 3] - 1] (* G. C. Greubel, Jan 20 2019 *)

CROSSREFS

Cf. A079385, A079386, A079366, A079367, A079368.

Sequence in context: A158349 A320478 A225302 * A260719 A291040 A089486

Adjacent sequences:  A079381 A079382 A079383 * A079385 A079386 A079387

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Feb 16 2003

EXTENSIONS

More terms from Mark Hudson (mrmarkhudson(AT)hotmail.com), Feb 17 2003

STATUS

approved

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Last modified February 21 02:57 EST 2019. Contains 320364 sequences. (Running on oeis4.)