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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 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.)