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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 (list; graph; refs; listen; history; text; internal format)
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

LINKS

Chai Wah Wu, Table of n, a(n) for n = 0..10000

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

Cf. A252867, A253050.

Sequence in context: A131406 A029440 A061337 * A103684 A105103 A086669

Adjacent sequences:  A253048 A253049 A253050 * A253052 A253053 A253054

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 01 2015

STATUS

approved

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Last modified August 5 03:00 EDT 2021. Contains 346457 sequences. (Running on oeis4.)