A104104 -id:A104104 - cp's OEIS frontend

A104106 a(1) = 1; thereafter, if A(k) = sequence of first 2^k -1 terms, then A(k+1) = A(k),1,A(k) if a(k) = 0, and A(k+1) = A(k),0,A(k) if a(k) = 1.

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

Offset: 1

Leroy Quet, Mar 04 2005

Robert Israel, Table of n, a(n) for n = 1..10000
Christian Krause, LODA program for A104106

Cf. A104104, A104105, A104107, A104108.

Cf. A089242.

a:= Vector(2^9-1):
a[1]:= 1;
for k from 1 to 8 do
  a[2^k]:= 1-a[k];
  a[2^k+1..2^(k+1)-1]:= a[1..2^k-1]
od:
convert(a,list); # Robert Israel, May 07 2018

f[l_]:=Join[l,1-{l[[Log[2,Length[l]+1]]]},l];Nest[f,{1},7] (* Ray Chandler, Apr 05 2009 *)

a(n) = A089242(n) mod 2. - Christian Krause, Mar 19 2021

Edited and extended by Ray Chandler, Apr 05 2009

A104105 a(1) = 1, if A(k) = sequence of first 2^k -1 terms and if B(k) is A(k) with 0's and 1's exchanged, then A(k+1) = A(k),1,B(k) if a(k) = 0, A(k+1) = A(k),0,B(k) if a(k) = 1.

Original entry on oeis.org

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

Offset: 1

Leroy Quet, Mar 04 2005

Cf. A104104, A104106, A104107, A104108.

f[l_]:=Join[l,1-{l[[Log[2,Length[l]+1]]]},1-l];Nest[f,{1},7] (* Ray Chandler, Apr 05 2009 *)

Edited and extended by Ray Chandler, Apr 05 2009

A104107 a(1) = 1, c(1)=1, if A(k) = sequence of first c(k) terms and if B(k) is A(k) with 0's and 1's exchanged, then A(k+1) = A(k)B(k) and c(k+1)= 2c(k) if a(k) = 0, A(k+1) = A(k),0,B(k) and c(k+1)= 2c(k)+1 if a(k) = 1.

Original entry on oeis.org

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

Offset: 1

Leroy Quet, Mar 04 2005

Cf. A104104, A104105, A104106, A104108.

f[l_]:=Join[l,If[l[[Floor[Log[2,Length[l]]]+1]]==0,{},{0}],1-l];Nest[f,{1},7] (* Ray Chandler, Apr 05 2009 *)

Edited and extended by Ray Chandler, Apr 05 2009

A104108 a(1) = 1, c(1)=1, if A(k) = sequence of first c(k) terms and if B(k) is A(k) with 0's and 1's exchanged, then A(k+1) = A(k)B(k) and c(k+1)= 2c(k) if a(k) = 1, A(k+1) = A(k),0,B(k) and c(k+1)= 2c(k)+1 if a(k) = 0.

Original entry on oeis.org

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

Offset: 1

Leroy Quet, Mar 04 2005

Cf. A104104, A104105, A104106, A104107.

f[l_]:=Join[l,If[l[[Floor[Log[2,Length[l]]]+1]]==1,{},{0}],1-l];Nest[f,{1},7] (* Ray Chandler, Apr 05 2009 *)

Edited and extended by Ray Chandler, Apr 05 2009

A112539 Half-baked Thue-Morse: at successive steps the sequence or its bit-inverted form is appended to itself.

Original entry on oeis.org

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

Offset: 1

Alexandre Losev, Dec 15 2005

			Triangle begins:
  1;
  0;
  1, 0;
  0, 1, 0, 1;
  1, 0, 1, 0, 0, 1, 0, 1;
  0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0;
  1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0;
  ...

Cf. A112865 (as +-1), A341389 (complement).

Cf. A104104, A010060.

s = {1}; Do[s = Join[s, Mod[s + 1, 2]]; s = Join[s, s], {n, 4}]; s (* Robert G. Wilson v, Dec 22 2005 *)

aiter(x) = my(s=[1]); for(i=1, x, s=concat(s, if(i%2, [1-e|e<-s], s))); s \\ Ruud H.G. van Tol, Jan 20 2025

s = [1]
for _ in range(4):
    s = s + [(x + 1) % 2 for x in s]
    s = s + s
print(s) # Robert C. Lyons, Jan 19 2025

More terms from Robert G. Wilson v, Dec 22 2005

cp's OEIS Frontend

A104106 a(1) = 1; thereafter, if A(k) = sequence of first 2^k -1 terms, then A(k+1) = A(k),1,A(k) if a(k) = 0, and A(k+1) = A(k),0,A(k) if a(k) = 1.

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A104105 a(1) = 1, if A(k) = sequence of first 2^k -1 terms and if B(k) is A(k) with 0's and 1's exchanged, then A(k+1) = A(k),1,B(k) if a(k) = 0, A(k+1) = A(k),0,B(k) if a(k) = 1.

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A104107 a(1) = 1, c(1)=1, if A(k) = sequence of first c(k) terms and if B(k) is A(k) with 0's and 1's exchanged, then A(k+1) = A(k)B(k) and c(k+1)= 2*c(k) if a(k) = 0, A(k+1) = A(k),0,B(k) and c(k+1)= 2*c(k)+1 if a(k) = 1.

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Mathematica

Extensions

A104108 a(1) = 1, c(1)=1, if A(k) = sequence of first c(k) terms and if B(k) is A(k) with 0's and 1's exchanged, then A(k+1) = A(k)B(k) and c(k+1)= 2*c(k) if a(k) = 1, A(k+1) = A(k),0,B(k) and c(k+1)= 2*c(k)+1 if a(k) = 0.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Extensions

A112539 Half-baked Thue-Morse: at successive steps the sequence or its bit-inverted form is appended to itself.

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Keywords

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Programs

Mathematica

PARI

Python

Extensions

A104107 a(1) = 1, c(1)=1, if A(k) = sequence of first c(k) terms and if B(k) is A(k) with 0's and 1's exchanged, then A(k+1) = A(k)B(k) and c(k+1)= 2c(k) if a(k) = 0, A(k+1) = A(k),0,B(k) and c(k+1)= 2c(k)+1 if a(k) = 1.

A104108 a(1) = 1, c(1)=1, if A(k) = sequence of first c(k) terms and if B(k) is A(k) with 0's and 1's exchanged, then A(k+1) = A(k)B(k) and c(k+1)= 2c(k) if a(k) = 1, A(k+1) = A(k),0,B(k) and c(k+1)= 2c(k)+1 if a(k) = 0.