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

1,2

Links

Table of n, a(n) for n=1..24.

Eric Weisstein's World of Mathematics, Continued Fraction.

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]

Crossrefs

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

Sequence in context: A248263 A201449 A205300 * A131902 A265029 A329065

Adjacent sequences: A065935 A065936 A065937 * A065939 A065940 A065941

Keyword

nonn

Author

Antti Karttunen, Dec 07 2001

Status

approved