A245536 Write n>=1 as either n=2^k-2^r with 0 <= r <= k-1, in which case a(2^k-2^r)=k-r-1, or as n=2^k-2^r+j with 2 <= r <= k-1, 1 <= j < 2^r-1, in which case a(2^k-2^r+j)=(k-r-1)*a(j).

0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 0, 1, 0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 0, 3, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 2, 0, 0, 2, 3, 0, 4, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2

Offset: 1

Author

N. J. A. Sloane, Jul 25 2014

Keywords

• nonn

Comments

Defined by the recurrence given in A245196, taking G(n)=n (n>=0) and m=1.

Changing G from [0,1,2,3,4,...] to [1,2,3,4,5,6,...] produces A038374.

Crossrefs

Cf. A245196, A038374.

Programs

Maple

G:=[seq(n,n=0..30)];
m:=1;
f:=proc(n) option remember; global m,G; local k,r,j,np;
   k:=1+floor(log[2](n)); np:=2^k-n;
   if np=1 then r:=0; j:=0; else r:=1+floor(log[2](np-1)); j:=2^r-np; fi;
   if j=0 then G[k-r-1+1]; else m*G[k-r-1+1]*f(j); fi;
end;
[seq(f(n),n=1..120)];