A103318 - OEIS

%I #12 Mar 29 2015 14:13:48

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

%C i=0 is always a solution.

%C a(n) is the number of 1's in (A103745(n) written in base 2). - _Philippe Deléham_, Apr 02 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>].

%F a(n) = A104234(2^n - n). - _Philippe Deléham_, Apr 21 2005

%e 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 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 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 For records see A034797. Cf. A103745.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Mar 21 2005