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.

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

Author

N. J. A. Sloane, May 23 2017

Keywords

• nonn

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

Examples

			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)
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000
• Ray Chandler, Table of n, a(n) for n = 1..1000000 (large gzipped file)

Crossrefs

Cf. A064736, A286290, A286291, A286293.

Formula

a(n) = A286290(n+1) - A286290(n) - 2. - M. F. Hasler, May 23 2017