A079381 Costé prime expansion of Euler's constant gamma (A001620).

2, 7, 13, 19, 89, 23, 11, 131, 73, 43, 37, 7, 11, 3, 3, 3, 3, 3, 5, 2, 7, 61, 251, 41, 13, 11, 7, 23, 29, 5, 13, 11, 3, 67, 29, 7, 5, 5, 2, 17, 5, 23, 7, 11, 2, 31, 29, 5, 5, 5, 3, 3, 5, 11, 5, 7, 7, 29, 17, 5, 2, 41, 13, 13, 11, 199, 157, 101, 37, 7, 127, 29, 11, 3, 3, 5, 17, 5, 7, 5, 2, 5

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(gamma);

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[EulerGamma] (* G. C. Greubel, Jan 20 2019 *)

Crossrefs

Cf. A079382, A079383, A079366-A079368.

Sequence in context: A231476 A138042 A053977 * A079382 A111354 A344959

Adjacent sequences: A079378 A079379 A079380 * A079382 A079383 A079384

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