A079375 Costé prime expansion of Pi^2 - 9.

2, 2, 3, 3, 5, 2, 19, 11, 29, 53, 149, 23, 7, 11, 5, 5, 3, 5, 5, 59, 11, 7, 7, 41, 19, 17, 23, 7, 5, 3, 7, 3, 11, 3, 3, 5, 2, 5, 3, 3, 53, 11, 5, 3, 41, 13, 29, 97, 13, 11, 2, 11, 5, 7, 7, 17, 5, 11, 3, 3, 7, 23, 53, 11, 5, 17, 5, 7, 3, 17

Offset: 0

Author

N. J. A. Sloane, Feb 16 2003

Keywords

• nonn
• easy

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

• Nathaniel Johnston, Table of n, a(n) for n = 0..5000
• A. Costé, Sur un système fibré lié à la suite des nombres premiers, Exper. Math., 11 (2002), 383-405.

Crossrefs

Cf. A079376, A079377, A079366, A079367, A079368.

Programs

Maple

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(Pi^2 - 9);

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[Pi^2 -9] (* G. C. Greubel, Jan 20 2019 *)