

A260393


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


2



0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1
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OFFSET

1


COMMENTS

Below, w* denotes the reversal of a word w, and "sequence" and "word" are interchangable. 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 examples.


LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = 1  A260390(n).


EXAMPLE

w(1) = 01, the initial word.
w(2) = 01010 ( = 01+0+10, where + = concatenation)
w(3) = 01010101010 = w(2)+1+w(2)*
w(4) = w(3)+1+w(3)*


MATHEMATICA

u[1] = {0, 1}; m[1] = {u[1][[1]]};
u[n_] := u[n] = Join[u[n  1], m[n  1], Reverse[u[n  1]]];
m[k_] := {u[k  1][[k]]}; u[8]


CROSSREFS

Cf. A260390.
Sequence in context: A285685 A287773 A173923 * A125122 A000035 A188510
Adjacent sequences: A260390 A260391 A260392 * A260394 A260395 A260396


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Jul 31 2015


STATUS

approved



