0,1

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.

The fxtbook contains a section "Synthetic iteration" with a fast algorithm to compute a function whose value at x=1/2 gives the constant 0.73216043306353283716459018717730446...whose binary value is 0.101110110110111011011101101110110110...

The evolution starting with 0 is:

0

1

101

1011101

10111011011011101

10111011011011101101110110111011011011101

Nest[ Flatten[ # /. {0 -> {1}, 1 -> {1, 0, 1}}] &, 0, 7] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 23 2005)

#! /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"

#! /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

Cf. A080764.

Sequence in context: A089045 A070749 A059778 this_sequence A131379 A090971 A105594

Adjacent sequences: A104518 A104519 A104520 this_sequence A104522 A104523 A104524

nonn

Joerg Arndt (arndt(AT)jjj.de), Apr 20 2005