A114986 Characteristic function of (A000201 prefixed with 0).

1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0

Offset

0,1

Comments

Fixed point of the morphism 0 -> 10, 1 -> 110, starting from {1}. - Paolo Xausa, Sep 22 2025

Links

Andrew Howroyd, Table of n, a(n) for n = 0..10000

Eric A. Lord, S. Ranganathan and Anandh Subramaniam, Stacking sequences and symmetry properties of trigonal vacancy-ordered phases, Phil. Mag. A 82 (2002) 255-268.

N. J. A. Sloane, Families of Essentially Identical Sequences, Mar 24 2021 (Includes this sequence)

Index entries for characteristic functions

Mathematica

A114986[n_] := Boole[n == 0 || FractionalPart[n*GoldenRatio]*GoldenRatio^2 > 1];
Array[A114986, 144, 0] (* or *)
First[SubstitutionSystem[{0 -> {1, 0}, 1 -> {1, 1, 0}}, {1}, {5}]] (* Paolo Xausa, Sep 22 2025 *)

Prog

(PARI) lista(n)={my(a=vector(n+1)); for(k=0, oo, my(m=(k+sqrtint(5*k^2))\2); if(m>n, break); a[1+m]=1); a} \\ Andrew Howroyd, Sep 21 2025

Crossrefs

Essentially the same as A005614. Cf. A096270, A189479.

The following sequences are all essentially the same, in the sense that they are simple transformations of each other, with A000201 as the parent: A000201, A001030, A001468, A001950, A003622, A003842, A003849, A004641, A005614, A014675, A022342, A088462, A096270, A114986, A124841. - N. J. A. Sloane, Mar 11 2021

Sequence in context: A014366 A014723 A365261 * A014282 A014555 A188017

Adjacent sequences: A114983 A114984 A114985 * A114987 A114988 A114989

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 28 2006

Status

approved