A215530 The limit of the string "0, 1" under the operation 'repeat string twice and append 0'.

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

Offset

0

Comments

Start of the first occurrence of k consecutive zeros: A123720 except the first term.

The limit of the string "0, 1" under the operation 'repeat string twice and append 1': 0 followed by b(n)=1-a(n+1).

Sum of the first 10^n terms c(n) begins: 0, 4, 34, 335, 3335, 33336, 333336, 3333338, 33333338, 333333339, 3333333339.

Links

Table of n, a(n) for n=0..86.

Example

01 -> 01010 -> 01010010100 -> 01010010100010100101000 etc.

Mathematica

rst[ll_] := Flatten[ll /. {x__ -> {x, x, 0}}]; Nest[rst[#] &, {0, 1}, 5] (* Harvey P. Dale, May 25 2015 *)

Prog

(Python)
TOP = 10000
a = [0]*TOP
b = [0]*TOP
a[1] = b[1] = 1
n = 2
while n*2+1<TOP:
  a[n:] = a[:n]
  a.append(0)
  b[n:] = b[:n]
  b.append(1)
  n += n+1
for i in range(n-1):
  print a[i],
  if b[i]!= 1 - a[i+1]:
    print 'error!'
    break
(Perl)
my $A = "01";
for (my $j = 1; $j < 10; $j++)  { $A .= $A . "0"; } print join(', ', split(//, $A)) . "\n";
# Joerg Arndt, Aug 15 2012

Crossrefs

Cf. A164349.

Sequence in context: A135993 A334414 A285966 * A241422 A189661 A145573

Adjacent sequences: A215527 A215528 A215529 * A215531 A215532 A215533

Keyword

nonn,easy

Author

Alex Ratushnyak, Aug 15 2012

Status

approved