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URL: https://oeis.org/A215530

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A215530
The limit of the string "0, 1" under the operation 'repeat string twice and append 0'.
3
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.
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 = 100
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], end = ', ')
if b[i]!= 1 - a[i+1]:
print('error!')
break
(Python)
def a_list(num_terms):
seq = [0, 1]
while len(seq) < num_terms:
seq += seq + [0]
return seq[:num_terms]
print(a_list(87)) # David Radcliffe, Jul 04 2025
(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
KEYWORD
nonn,easy
AUTHOR
Alex Ratushnyak, Aug 15 2012
STATUS
approved