%I A040026
%S A040026 1,1,3,1,5,3,7,1,9,5,11,3,13,7,15,1,17,9,19,5,21,11,23,9,25,13,27,7,29,
               15,
%T A040026 31,1,33,17,35,9,37,19,39,15,41,21,43,11,45,23,47,15,49,25,51,13,53,
%U A040026 27,55,7,57,29,59,15,61,31,63,1,65,33,67,17,69,35,71,9,73,37,75,19
%V A040026 1,1,3,1,5,3,7,1,9,5,11,-3,13,7,15,1,17,9,19,5,21,11,23,9,25,13,27,-7,
               29,15,
%W A040026 31,1,33,17,35,9,37,19,39,-15,41,21,43,-11,45,23,47,-15,49,25,51,13,53,
%X A040026 27,55,-7,57,29,59,-15,61,31,63,1,65,33,67,17,69,35,71,9,73,37,75,-19
%N A040026 If n=r*2^s, r odd, then a(n)=t*r, where t is smallest (in magnitude) 
               number such that 1=t*r+u*2^s.
%D A040026 J. Neukirch, Class Field Theory, Springer, p. 1.
%e A040026 24=3*2^3, 1=3*3-1*2^3, a(24)=3*3=9.
%o A040026 (C:) for(n=1; n<=100; n++) { r=n; s=1; while((r&1)==0) { r>>=1; s<<=1; 
               } for(t=1; t<9999; t++) { if(((t*r-1)%s)==0) { printf("%d,",t*r); 
               break; } if(((t*r+1)%s)==0) { printf("%d,",-t*r); break; } } if((n%10)==0) 
               printf("\n"); if(t==9999) exit(0); //"not found": error }
%Y A040026 |a(n)| differs from A000265, as a(24)=9.
%Y A040026 Sequence in context: A161955 A000265 A106617 this_sequence A106609 A093474 
               A030101
%Y A040026 Adjacent sequences: A040023 A040024 A040025 this_sequence A040027 A040028 
               A040029
%K A040026 sign,easy,nice
%O A040026 1,3
%A A040026 N. J. A. Sloane (njas(AT)research.att.com).
%E A040026 More terms from Arlin Anderson (starship1(AT)gmail.com)