login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A341256 Concatenation of all 01-words in the order induced by A004526; see Comments. 7
0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

Let s = (s(n)) be a strictly increasing sequence of positive integers with infinite complement, t = (t(n)). For n >=1, let s'(n) be the number of s(i) that are <= n-1 and let t'(n) be the number of t(i) that are <= n-1. Define w(1) = 0, w(t(1)) = 1, and w(n) = 0w(s'(n)) if n is in s, and w(n) = 1w(t'(n)) if n is in t. Then (w(n)) is the "s-induced ordering" of all 01-words.

****

Guide to related sequences:

   s       01-words ordered by s            positions of palindromes

A092754    A076478 (lexicographic order)    A341257

A004526    A341256                          A341257

A000201    A341258                          A341333

A016777    A341334                          A342750

A001651    A342753                          A342790

A032766    A342910                          A344166

LINKS

Table of n, a(n) for n=1..86.

FORMULA

To generate successive words w(n), if n is in s, spell w(n) as 0 suffixed by the first w(k) that does not already suffix a word beginning with 0; otherwise, spell w(n) as 1 suffixed by the first w(k) that does not already suffix a word beginning with 1.

EXAMPLE

The first 20 words: 0, 1, 00, 10, 01, 11, 000, 100, 010, 110, 001, 101, 011, 111, 0000, 1000, 0100, 1100, 0010, 1010.

MATHEMATICA

z = 80; s = Table[2 n - 1, {n, 1, z}]; (* A004526 *)

t = Complement[Range[Max[s]], s]; (* A005843 *)

s1[n_] := Length[Intersection[Range[n - 1], s]];

t1[n_] := n - 1 - s1[n]; (* A023416 *)

w[1] = {0}; w[t[[1]]] = {1};

w[n_] := If[MemberQ[s, n], Join[{0}, w[s1[n]]], Join[{1}, w[t1[n]]]]

tt = Table[w[n], {n, 1, z}]  (* 01-words, in order *)

Flatten[tt] (* A341256 *)

CROSSREFS

Cf. A004526, A005843, A023416, A092754, A341257.

Sequence in context: A051065 A091445 A091446 * A270742 A164349 A094186

Adjacent sequences:  A341253 A341254 A341255 * A341257 A341258 A341259

KEYWORD

nonn

AUTHOR

Clark Kimberling, Mar 16 2021

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 24 12:38 EDT 2021. Contains 347642 sequences. (Running on oeis4.)