A105023 - OEIS

%I #14 May 05 2020 05:34:53

%S 0,2,4,2,0,10,4,2,0,2,4,2,16,10,4,2,0,2,4,2,0,10,4,2,0,2,4,34,16,10,4,

%T 2,0,2,4,2,0,10,4,2,0,2,4,2,16,10,4,2,0,2,4,2,0,10,4,2,0,2,68,34,16,

%U 10,4,2,0,2,4,2,0,10,4,2,0,2,4,2,16,10,4,2,0,2,4,2,0,10,4,2,0,2,4,34,16,10,4

%N a(n) = A102370(n) - n. Or, 2*A103185(n).

%C When written in base 2 as a right justified table, columns have periods 1, 2, 4, 8, ... - _Philippe Deléham_, Apr 21 2005

%H David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [<a href="http://neilsloane.com/doc/slopey.pdf">pdf</a>, <a href="http://neilsloane.com/doc/slopey.ps">ps</a>].

%H David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL8/Sloane/sloane300.html">Sloping binary numbers: a new sequence related to the binary numbers</a>, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp.

%F a(n) = Sum_{ k >= 1 such that n + k == 0 mod 2^k } 2^k.

%e Has a natural decomposition into blocks: 0; 2; 4, 2, 0; 10, 4, 2, 0, 2, 4, 2; 16, 10, 4, 2, 0, 2, 4, 2, 0, 10, 4, 2, 0, 2, 4; 34, 16, 10, 4, ... where the leading term in each block is given by A105024.

%p s:= proc (n) local t1, l; t1 := 0; for l to n do if `mod`(n+l,2^l) = 0 then t1 := t1+2^l end if end do; t1 end proc;

%Y Cf. A102370, A103185, A105024.

%K nonn,base

%O 0,2

%A _N. J. A. Sloane_, Apr 03 2005