This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A065938 #6 Feb 16 2025 08:32:45 %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="https://mathworld.wolfram.com/ContinuedFraction.html">Continued Fraction.</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. %K A065938 nonn %O A065938 1,2 %A A065938 _Antti Karttunen_, Dec 07 2001