A260444 Infinite palindromic word (a(1),a(2),a(3),...) with initial word w(1) = (1,0,0) and midword sequence (a(n)); see A260390.

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

Offset

1

Comments

Below, w* denotes the reversal of a word w, and "sequence" and "word" are interchangeable. An infinite word is palindromic if it has infinitely many initial subwords w such that w = w*.

Many infinite palindromic words (a(1),a(2),...) are determined by an initial word w and a midword sequence (m(1),m(2),...) of palindromes, as follows: for given w of length k, take w(1) = w = (a(1),a(2),...,a(k)). Form the palindrome w(2) = w(1)m(1)w(1)* by concatenating w(1), m(1), and w(1)*. Continue inductively; i.e., w(n+1) = w(n)m(n)w(n)* for all n >= 1. See A260390 for a guide to related sequences.

Links

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

Example

w(1) = 100, the initial word.
w(2) = 1001001 ( = 100+1+001, where + = concatenation)
w(3) = w(2)+0+w(2)*
w(4) = w(3)+1+w(3)*

Mathematica

u[1] = {1, 0, 0}; m[1] = {u[1][[1]]};
u[n_] := u[n] = Join[u[n - 1], m[n - 1], Reverse[u[n - 1]]]
m[k_] := {u[k][[k]]}
v = u[6]  (* A260444 *)

Crossrefs

Cf. A260390.

Sequence in context: A245485 A068429 A285208 * A289034 A011747 A089013

Adjacent sequences: A260441 A260442 A260443 * A260445 A260446 A260447

Keyword

nonn,easy

Author

Clark Kimberling, Oct 31 2015

Status

approved