%I #5 Jan 07 2013 15:02:07
%S 1,6,14,7,120,248,16160,1019,127,32640,65408,16373,8386032,4194056,
%T 4194239,32767,2147450880,4294934528,4611672824287851743,268435343,
%U 8796091842564,1125899889968159,70368744112268,70368744161279
%N Position of sqrt(n) in the mapping N2QuQR1 given in A065936.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ContinuedFraction.html">Continued Fraction.</a>
%p [seq(frac2position_in_0_1_SB_tree(sqrt_n_confrac2binfrac(j)),j=1..40)];
%p 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 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 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 Cf. A003285. N2QuQR1(a[n])^2 = n, see A065936. For frac2position_in_0_1_SB_tree see A065658. Cf. also A065939.
%K nonn
%O 1,2
%A _Antti Karttunen_, Dec 07 2001