login
A258869
Expansion of 1 to the basis 1.880000478655... (A127583).
0
1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0
OFFSET
1
COMMENTS
Eventually periodic: [1, 1, 1, 0, 0, 1, 0, 1, 1], followed by period 7, repeat: [1, 0, 0, 1, 0, 1, 0].
LINKS
J.-P. Allouche, C. Frougny, K. G. Hare, On univoque Pisot numbers, arXiv:math/0610681 [math.NT], (23-October-2006)
J.-P. Allouche, C. Frougny, K. G. Hare, On univoque Pisot numbers, Math. Comp. 76 (2007), 1639-1660.
FORMULA
Sum_{k>=1} r^k = 1 where r = 1/1.880000478655... .
From Chai Wah Wu, Jun 04 2016: (Start)
a(n) = a(n-7) for n > 15.
G.f.: x*(x^15 - x^5 - x^2 - x - 1)/(x^7 - 1). (End)
MATHEMATICA
Join[{1, 1, 1, 0, 0, 1, 0, 1, 1}, PadRight[{}, 120, {1, 0, 0, 1, 0, 1, 0}]] (* Vincenzo Librandi, Jun 14 2015 *)
PROG
(Magma) [1, 1, 1, 0, 0, 1, 0, 1, 1] cat &cat[[1, 0, 0, 1, 0, 1, 0]: n in [0..17]]; // Vincenzo Librandi, Jun 14 2015
CROSSREFS
Cf. A127583 (smallest univoque Pisot Number).
Sequence in context: A110037 A244528 A145379 * A128810 A355946 A123272
KEYWORD
nonn,easy
AUTHOR
Joerg Arndt, Jun 13 2015
STATUS
approved