A065938 Position of sqrt(n) in the mapping N2QuQR1 given in A065936.

1, 6, 14, 7, 120, 248, 16160, 1019, 127, 32640, 65408, 16373, 8386032, 4194056, 4194239, 32767, 2147450880, 4294934528, 4611672824287851743, 268435343, 8796091842564, 1125899889968159, 70368744112268, 70368744161279

Offset: 1

Author

Antti Karttunen, Dec 07 2001

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Continued Fraction.

Crossrefs

Cf. A003285. N2QuQR1(a[n])^2 = n, see A065936. For frac2position_in_0_1_SB_tree see A065658. Cf. also A065939.

Programs

Maple

[seq(frac2position_in_0_1_SB_tree(sqrt_n_confrac2binfrac(j)),j=1..40)];
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;
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;
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]