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A253051
A compressed version of A253050 (A252867 mod 2): replace every substring 01 in A253050 with 1, every 001 with 2, every 0001 with 3, every 00001 with 4, etc.
3
1, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 3, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1
OFFSET
0,3
COMMENTS
The replacements are to be done in reverse order, of course, starting with the longest string of 0 and working backwards.
The first 4 appears at about term 3879. When does the first 5 appear?
Equivalent to run lengths of 0's. - Chai Wah Wu, Jan 01 2015
a(n) < 5 for n <= 10^6. - Chai Wah Wu, Jan 14 2015
PROG
(Python)
A253051_list, c, l1, l2, s, b = [1], 1, 2, 1, 3, set()
for _ in range(10**6):
....i = s
....while True:
........if not (i in b or i & l1) and i & l2:
............if i & 1:
................A253051_list.append(c)
................c = 0
............else:
................c += 1
............l2, l1 = l1, i
............b.add(i)
............while s in b:
................b.remove(s)
................s += 1
............break
........i += 1 # Chai Wah Wu, Jan 01 2015
CROSSREFS
Sequence in context: A029440 A061337 A352767 * A103684 A105103 A377648
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 01 2015
STATUS
approved