A247459 Numbers k such that d(r,k) = d(s,k), where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {3*sqrt(2)}, and { } = fractional part.
1, 3, 5, 7, 8, 9, 10, 11, 13, 15, 16, 17, 19, 21, 23, 25, 27, 29, 30, 31, 32, 33, 34, 36, 38, 39, 40, 42, 43, 44, 46, 48, 50, 51, 53, 54, 56, 57, 58, 59, 61, 62, 64, 66, 68, 70, 72, 73, 74, 75, 76, 78, 80, 81, 82, 84, 86, 87, 89, 91, 93, 94, 96, 97, 99, 101
Offset: 1
Examples
{1*sqrt(2)} has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1,...
{3*sqrt(2)} has binary digits 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1,...
so that a(1) = 1 and a(2) = 3.
Links
- Clark Kimberling, Table of n, a(n) for n = 1..1000
Programs
-
Mathematica
z = 200; r = FractionalPart[Sqrt[2]]; s = FractionalPart[3*Sqrt[2]]; u = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[r, 2, z]]; v = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[s, 2, z]]; t = Table[If[u[[n]] == v[[n]], 1, 0], {n, 1, z}]; Flatten[Position[t, 1]] (* A247459 *) Flatten[Position[t, 0]] (* A247460 *)
Comments