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A286292
The first differences of A286291 (one of the bisections of A064736) appears to consist of runs of 1 followed by singleton 2's; this sequence gives the lengths of these runs.
5
3, 4, 6, 13, 19, 14, 16, 18, 31, 37, 26, 28, 30, 32, 34, 55, 61, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 100, 106, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 163, 169, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138
OFFSET
1,1
COMMENTS
The steps of 2 occur when the corresponding integer is not in A286291 because it already occurred in A286290 [numbers of the form m(m+1) (m & m+1 not occurring earlier) or (m-1)(m+1) with m occurring earlier]. Accordingly, the present sequence equals first differences of A286290, minus 2. - M. F. Hasler, May 23 2017
LINKS
Ray Chandler, Table of n, a(n) for n = 1..1000000 (large gzipped file)
FORMULA
a(n) = A286290(n+1) - A286290(n) - 2. - M. F. Hasler, May 23 2017
EXAMPLE
A064736: 1, 2, 6, 3, 12, 4, 20, 5, 35, 7, 56, 8, 72, 9, 90, 10, 110, ...
Bisect: 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, ... (A286291)
Differences: 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, ...
Runs: 3, 1, 4, 1, 6, 1, 13, 1, 19, 1, 14, 1, 16, 1, 18, 1, 31, 1, 37, 1, ...
Bisect: 3, 4, 6, 13, 19, 14, 16, 18, 31, 37, 26, 28, 30, 32, 34, 55, ... (this sequence)
From M. F. Hasler, May 23 2017: (Start)
Another approach:
A286290 = 1, 6, 12, 20, 35, 56, 72, 90, 110, 143, 182, 210, 240, 272, 306, 342, ...
1st Diff.: 5, 6, 8, 15, 21, 16, 18, 20, 33, 39, 28, 30, 32, 34, 36, ...
minus 2 = 3, 4, 6, 13, 19, 14, 16, 18, 31, 37, 26, 28, 30, 32, 34, ... (this sequence). (End)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 23 2017
STATUS
approved