cp's OEIS Frontend

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.

%I A286292 #25 May 27 2017 07:09:51
%S A286292 3,4,6,13,19,14,16,18,31,37,26,28,30,32,34,55,61,42,44,46,48,50,52,54,
%T A286292 56,58,60,62,64,100,106,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,
%U A286292 102,104,106,163,169,114,116,118,120,122,124,126,128,130,132,134,136,138
%N 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.
%C A286292 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
%H A286292 Ray Chandler, <a href="/A286292/b286292.txt">Table of n, a(n) for n = 1..10000</a>
%H A286292 Ray Chandler, <a href="/A286292/a286292_1M.gz">Table of n, a(n) for n = 1..1000000</a> (large gzipped file)
%F A286292 a(n) = A286290(n+1) - A286290(n) - 2. - _M. F. Hasler_, May 23 2017
%e A286292 A064736: 1, 2, 6, 3, 12, 4, 20, 5, 35, 7, 56, 8, 72, 9, 90, 10, 110, ...
%e A286292 Bisect: 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, ... (A286291)
%e A286292 Differences: 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, ...
%e A286292 Runs: 3, 1, 4, 1, 6, 1, 13, 1, 19, 1, 14, 1, 16, 1, 18, 1, 31, 1, 37, 1, ...
%e A286292 Bisect: 3, 4, 6, 13, 19, 14, 16, 18, 31, 37, 26, 28, 30, 32, 34, 55, ... (this sequence)
%e A286292 From _M. F. Hasler_, May 23 2017: (Start)
%e A286292 Another approach:
%e A286292 A286290 = 1, 6, 12, 20, 35, 56, 72, 90, 110, 143, 182, 210, 240, 272, 306, 342, ...
%e A286292 1st Diff.: 5, 6,  8,  15, 21, 16, 18, 20,  33,  39,  28,  30,  32,  34, 36, ...
%e A286292 minus 2 =  3, 4,  6,  13, 19, 14, 16, 18,  31,  37,  26,  28,  30,  32, 34, ... (this sequence). (End)
%Y A286292 Cf. A064736, A286290, A286291, A286293.
%K A286292 nonn
%O A286292 1,1
%A A286292 _N. J. A. Sloane_, May 23 2017