A258869 Expansion of 1 to the basis 1.880000478655... (A127583).

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

Table of n, a(n) for n=1..107.

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.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,1).

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

Adjacent sequences: A258866 A258867 A258868 * A258870 A258871 A258872

Keyword

nonn,easy

Author

Joerg Arndt, Jun 13 2015

Status

approved