A079378 Costé prime expansion of (sqrt(5)-1)/2.

2, 5, 7, 5, 5, 2, 11, 5, 2, 13, 11, 5, 5, 5, 5, 2, 5, 3, 5, 11, 2, 79, 37, 11, 5, 3, 7, 17, 59, 23, 11, 2, 17, 7, 3, 7, 7, 383, 337, 67, 13, 19, 47, 23, 41, 17, 17, 13, 67, 71, 47, 17, 11, 19, 73, 53, 17, 13, 37, 19, 11, 5, 13, 29, 43, 47, 17, 5, 5, 11, 3, 3, 17, 5, 97, 29, 11, 3, 3, 3, 7

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((sqrt(5)-1)/2);

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[(Sqrt[5] -1)/2] (* G. C. Greubel, Jan 20 2019 *)

Crossrefs

Cf. A079379, A079380, A079366, A079367, A079368.

Sequence in context: A082880 A257321 A011038 * A066035 A329283 A296168

Adjacent sequences: A079375 A079376 A079377 * A079379 A079380 A079381

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