|
| |
|
|
A104521
|
|
Fixed point of the morphism 0->{1}, 1->{1,0,1}.
|
|
0
| |
|
|
1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,1
|
|
|
COMMENTS
| A080764 and this sequence contain (arbitrarily?) long common substrings.
Zak Seidov points out (Mar 17 2006) that essentially the same sequence arises from the following process: Start with {0,1}; between each pair of digits, insert their sum written in binary. We get successively:
{0,1,1}
{0,1,1,1,0,1}
{0,1,1,1,0,1,1,0,1,1,0,1,1}
{0,1,1,1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,1,1,0,1,1,0,1,1,1,0,1}, etc.,
which is the current sequence without the initial 1.
|
|
|
LINKS
| Joerg Arndt, fxtbook, section 38.12.1 "Pell palindromes", p.759 (fast algorithm to compute a function whose value at x=1/2 gives the constant 0.7321604330... whose binary value is 0.1011101101101...)
|
|
|
EXAMPLE
| The evolution starting with 0 is:
0
1
101
1011101
10111011011011101
10111011011011101101110110111011011011101
|
|
|
MATHEMATICA
| Nest[ Flatten[ # /. {0 -> {1}, 1 -> {1, 0, 1}}] &, 0, 7] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 23 2005)
|
|
|
PROG
| #! /usr/bin/env zsh function N { local w=$1; for (( i=0; i<7; i+=1 )); do echo $w; w=$(echo $w | S); done } function S { sed 's/1/1_1/g; s/0/1/g; s/_/0/g; ' } # 0->1, 1->101 N "0" - Joerg Arndt (arndt(AT)jjj.de), Apr 24 2005
|
|
|
CROSSREFS
| Cf. A080764.
Sequence in context: A089045 A070749 A059778 * A131379 A181656 A090971
Adjacent sequences: A104518 A104519 A104520 * A104522 A104523 A104524
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Joerg Arndt (arndt(AT)jjj.de), Apr 20 2005
|
| |
|
|
