|
| |
|
|
A079366
|
|
Costé prime expansion of Pi - 3.
|
|
28
|
|
|
|
11, 2, 11, 5, 5, 2, 5, 3, 17, 11, 3, 3, 11, 3, 3, 11, 5, 3, 23, 7, 5, 97, 29, 37, 107, 127, 29, 17, 409, 127, 11, 29, 5, 67, 19, 43, 31, 19, 103, 59, 29, 7, 3, 11, 11, 5, 47, 29, 11, 3, 5, 5, 3, 17, 5, 29, 11, 3, 3, 3, 3, 5, 5, 61, 151, 58889, 1877, 983, 757, 163
(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).
Costé prime expansion = Engel expansion where all terms must be primes (cf. A006784).
|
|
|
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.
Index entries for sequences related to Engel expansions
|
|
|
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-3);
|
|
|
MATHEMATICA
|
$MaxExtraPrecision = 40; 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 <= 70, i++, AppendTo[t1, p = P[y]]; y = p*y-1]; t1]; F[Pi-3] (* Jean-François Alcover, Dec 16 2013, translated from Maple *)
|
|
|
CROSSREFS
|
Cf. A079367, A079368. Also A079369-A079389.
Sequence in context: A284212 A273877 A066795 * A351653 A226110 A323484
Adjacent sequences: A079363 A079364 A079365 * A079367 A079368 A079369
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
N. J. A. Sloane, Feb 15 2003
|
|
|
STATUS
|
approved
|
| |
|
|
