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A215530 The limit of the string "0, 1" under the operation 'repeat string twice and append 0'. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A073424 A135993 A285966 * A241422 A189661 A145573

Adjacent sequences:  A215527 A215528 A215529 * A215531 A215532 A215533

KEYWORD

nonn,easy

AUTHOR

Alex Ratushnyak, Aug 15 2012

STATUS

approved

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Last modified October 15 07:56 EDT 2019. Contains 328026 sequences. (Running on oeis4.)