|
%I #11 Sep 26 2014 17:23:56
%S 1,2,4,8,10,11,13,14,15,18,21,25,26,27,31,34,35,36,38,39,40,42,43,44,
%T 46,47,50,51,53,54,55,59,60,63,64,65,68,70,71,72,73,77,78,79,80,83,84,
%U 85,86,87,92,94,95,97,100,103,107,109,110,112,114,118,119
%N Numbers k such that d(r,k) != d(s,k), where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {sqrt(3)}, and { } = fractional part.
%C Every positive integer lies in exactly one of the sequences A247454 and A247324.
%H Clark Kimberling, <a href="/A247324/b247324.txt">Table of n, a(n) for n = 1..1000</a>
%e {sqrt(2)} has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1,...
%e {sqrt(3)} has binary digits 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0,..
%e so that a(1) = 1 and a(2) = 2.
%t z = 200; r = FractionalPart[Sqrt[2]]; s = FractionalPart[Sqrt[3]];
%t u = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[r, 2, z]];
%t v = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[s, 2, z]];
%t t = Table[If[u[[n]] == v[[n]], 1, 0], {n, 1, z}];
%t Flatten[Position[t, 1]] (* A247454 *)
%t Flatten[Position[t, 0]] (* A247324 *)
%Y Cf. A246356, A247454.
%K nonn,easy,base
%O 1,2
%A _Clark Kimberling_, Sep 17 2014
|
