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

1,1

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..10000

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

Cf. A064736, A286290, A286291, A286293.

Sequence in context: A102733 A032712 A226792 * A180647 A318345 A357356

Adjacent sequences: A286289 A286290 A286291 * A286293 A286294 A286295

Keyword

nonn

Author

N. J. A. Sloane, May 23 2017

Status

approved