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A112639
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a(n) = floor(r^n) where r is the smallest Pisot number (real root r=1.3247179... of x^3-x-1).
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1
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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
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OFFSET
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0,4
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COMMENTS
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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]
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LINKS
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Table of n, a(n) for n=0..46.
Andrei Vieru, Pisot Numbers and Primes, arXiv:1205.1054v1 [math.NT], Apr 04 2012
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MATHEMATICA
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r = Solve[x^3 - x - 1 == 0, x][[1, 1, 2]]; Table[Floor[r^n], {n, 0, 50}] (* T. D. Noe, Jan 30 2012 *)
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PROG
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(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 */
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula, Mar 31 2006
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EXTENSIONS
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Completely edited by Joerg Arndt, Jan 29 2012
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STATUS
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approved
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