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A112639 a(n) = floor(r^n) where r is the smallest Pisot number (real root r=1.3247179... of x^3-x-1). 1
1, 1, 1, 2, 3, 4, 5, 7, 9, 12, 16, 22, 29, 38, 51, 67, 89, 119, 157, 209, 276, 366, 486, 643, 853, 1130, 1496, 1983, 2626, 3480, 4610, 6106, 8090, 10716, 14196, 18807, 24913, 33004, 43721, 57917, 76725, 101638, 134643, 178364, 236281, 313007, 414645 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Andrei Vieru says "We define and study a transform whose iterates bring to the fore interesting relations between Pisot numbers and primes. Although the relations we describe are general, they take a particular form in the Pisot limit points. We give three elegant formulas, which permit to locate on the whole semi-line all limit points that are not integer powers of other Pisot numbers." [Jonathan Vos Post, May 07 2012]

LINKS

Table of n, a(n) for n=0..46.

Andrei Vieru, Pisot Numbers and Primes, arXiv:1205.1054v1 [math.NT], Apr 04 2012

MATHEMATICA

r = Solve[x^3 - x - 1 == 0, x][[1, 1, 2]]; Table[Floor[r^n], {n, 0, 50}] (* T. D. Noe, Jan 30 2012 *)

PROG

(PARI)

default(realprecision, 110);

default(format, "g.15");

r=real(polroots(x^3-x-1)[1])

v=vector(66, n, floor(r^(n-1)) )  /* Joerg Arndt, Jan 29 2012 */

CROSSREFS

Cf. A060006 (decimal expansion of r=1.32471795724475...).

Cf. A051016, A051017.

Cf. A205579 (definition using round() instead of floor()).

Sequence in context: A117597 A241336 A233522 * A290137 A336351 A241818

Adjacent sequences:  A112636 A112637 A112638 * A112640 A112641 A112642

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Mar 31 2006

EXTENSIONS

Completely edited by Joerg Arndt, Jan 29 2012

STATUS

approved

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Last modified May 24 14:01 EDT 2022. Contains 354036 sequences. (Running on oeis4.)