

A260456


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


3



1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 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  A260455(n).


EXAMPLE

w(1) = 1, the initial word.
w(2) = 101 ( = 1+0+1, where + = concatenation)
w(3) = 101101 = w(2)+null+w(2)*, where null  the empty word
w(4) = w(3)+0+w(3)*


MATHEMATICA

u[1] = {1}; m[1] = {0}; u[n_] := u[n] = Join[u[n  1], m[n  1], Reverse[u[n  1]]];
m[k_] := If[OddQ[k], {0}, {}] (* midword seq: 1, null, 1, null, 1, null, ... *)
u[8]


CROSSREFS

Cf. A260390, A260455.
Sequence in context: A249866 A128174 A096055 * A125144 A115198 A005614
Adjacent sequences: A260453 A260454 A260455 * A260457 A260458 A260459


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Aug 29 2015


STATUS

approved



