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A246357
Numbers k such that d(r,k) = 0 and d(s,k) = 1, where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {sqrt(3)}, and { } = fractional part.
4
1, 4, 8, 10, 11, 14, 15, 21, 25, 38, 42, 47, 51, 54, 55, 59, 60, 63, 64, 70, 72, 78, 83, 85, 86, 92, 100, 107, 109, 119, 121, 128, 134, 136, 147, 148, 150, 153, 157, 162, 168, 169, 173, 182, 183, 184, 198, 200, 209, 211, 214, 215, 218, 226, 227, 229, 241
OFFSET
1,2
COMMENTS
Every positive integer lies in exactly one of these: A246356, A246357, A246358, A247356.
LINKS
EXAMPLE
{sqrt(2)} has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1,...
{sqrt(3)} has binary digits 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0,..
so that a(1) = 1 and a(2) = 4.
MATHEMATICA
z = 500; r = FractionalPart[Sqrt[2]]; s = FractionalPart[Sqrt[3]];
u = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[r, 2, z]]
v = Flatten[{ConstantArray[0, -#[[2]]], #[[1]]}] &[RealDigits[s, 2, z]]
t1 = Table[If[u[[n]] == 0 && v[[n]] == 0, 1, 0], {n, 1, z}];
t2 = Table[If[u[[n]] == 0 && v[[n]] == 1, 1, 0], {n, 1, z}];
t3 = Table[If[u[[n]] == 1 && v[[n]] == 0, 1, 0], {n, 1, z}];
t4 = Table[If[u[[n]] == 1 && v[[n]] == 1, 1, 0], {n, 1, z}];
Flatten[Position[t1, 1]] (* A246356 *)
Flatten[Position[t2, 1]] (* A246357 *)
Flatten[Position[t3, 1]] (* A246358 *)
Flatten[Position[t4, 1]] (* A247356 *)
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Clark Kimberling, Sep 17 2014
STATUS
approved