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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
OFFSET
0,4
LINKS
Andrei Vieru, Pisot Numbers and Primes, arXiv:1205.1054 [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. A205579 (definition using round() instead of floor()).
Sequence in context: A117597 A241336 A233522 * A375185 A290137 A336351
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Mar 31 2006
EXTENSIONS
Completely edited by Joerg Arndt, Jan 29 2012
STATUS
approved