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A103318 Number of solutions i in range [0,n-1] to i == 0 mod 2^(n-i).

%I A103318 #12 Mar 29 2015 14:13:48
%S A103318 1,1,2,1,2,2,2,1,2,2,3,1,2,2,2,1,2,2,3,2,2,2,2,1,2,2,3,1,2,2,2,1,2,2,
%T A103318 3,2,3,2,2,1,2,2,3,1,2,2,2,1,2,2,3,2,2,2,2,1,2,2,3,1,2,2,2,1,2,2,3,2,
%U A103318 3,3,2,1,2,2,3,1,2,2,2,1,2,2,3,2,2,2,2,1,2,2,3,1,2,2,2,1,2,2,3
%N A103318 Number of solutions i in range [0,n-1] to i == 0 mod 2^(n-i).
%C A103318 i=0 is always a solution.
%C A103318 a(n) is the number of 1's in (A103745(n) written in base 2). - _Philippe Deléham_, Apr 02 2005
%H A103318 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>].
%F A103318 a(n) = A104234(2^n - n). - _Philippe Deléham_, Apr 21 2005
%e A103318 For n = 11 solutions are i = 0, 8 and 10. Four solutions occur for the first time at n = 2059: they are i = 0, 2048, 2056, 2058. Five solutions occur for the first time at n = 2^2059 + 2059 (see A034797).
%p A103318 f:= proc (n) local t1, l; t1 := 0; for l to n do if `mod`(n-l,2^l) = 0 then t1 := t1+1 end if end do; t1 end proc;
%t A103318 f[n_] := Block[{c = 1, k = Max[1, n - Floor[ Log[2, n] + 2]]}, While[k < n, If[ Mod[k, 2^(n - k)] == 0, c++ ]; k++ ]; c]; Table[ f[n], {n, 105}] (* _Robert G. Wilson v_, Mar 21 2005 *)
%Y A103318 For records see A034797. Cf. A103745.
%K A103318 nonn
%O A103318 1,3
%A A103318 _N. J. A. Sloane_, Mar 21 2005