Search: id:A065938
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%I A065938
%S A065938 1,6,14,7,120,248,16160,1019,127,32640,65408,16373,8386032,4194056,
%T A065938 4194239,32767,2147450880,4294934528,4611672824287851743,268435343,
%U A065938 8796091842564,1125899889968159,70368744112268,70368744161279
%N A065938 Position of sqrt(n) in the mapping N2QuQR1 given in A065936.
%H A065938 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               ContinuedFraction.html">Link to a section of The World of Mathematics.</
               a>
%p A065938 [seq(frac2position_in_0_1_SB_tree(sqrt_n_confrac2binfrac(j)),j=1..40)];
%p A065938 sqrt_n_confrac2binfrac := proc(n) local c,t; c := CONFRACS_FOR_sqrt_N[n]; 
               t := `if`((1 = nops(c)),[],`if`((0 = (nops(c) mod 2)),[op(c[2..nops(c)]),
               op(c[2..nops(c)])],c[2..nops(c)])); RETURN( (((2^c[1])-1) + `if`(1 
               = nops(c),0,(runcounts2binexp0(t) / ((2^(convert(t,`+`)))-1)))) / 
               (2^c[1])); end;
%p A065938 runcounts2binexp0 := proc(c) local i,e,n; n := 0; for i from 0 to nops(c)-1 
               do e := c[i+1]; n := ((2^e)*n) + ((i mod 2)*((2^e)-1)); od; RETURN(n); 
               end;
%p A065938 CONFRACS_FOR_sqrt_N := [[1], [1, 2], [1, 1, 2], [2], [2, 4], [2, 2, 4], 
               [2, 1, 1, 1, 4], [2, 1, 4], [3], [3, 6], etc., adapted from Weisstein's 
               encyclopedia entry for Continued Fractions]
%Y A065938 Cf. A003285. N2QuQR1(a[n])^2 = n, see A065936. For frac2position_in_0_1_SB_tree 
               see A065658. Cf. also A065939.
%Y A065938 Sequence in context: A042641 A042285 A041070 this_sequence A131902 A079010 
               A015822
%Y A065938 Adjacent sequences: A065935 A065936 A065937 this_sequence A065939 A065940 
               A065941
%K A065938 nonn
%O A065938 1,2
%A A065938 Antti Karttunen Dec 07 2001

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