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A246358 Numbers k such that d(r,k) = 1 and d(s,k) = 0, where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {sqrt(3)}, and { } = fractional part. 4
2, 13, 18, 26, 27, 31, 34, 35, 36, 39, 40, 43, 44, 46, 50, 53, 65, 68, 71, 73, 77, 79, 80, 84, 87, 94, 95, 97, 103, 110, 112, 114, 118, 123, 124, 126, 127, 132, 133, 135, 142, 143, 145, 146, 152, 155, 156, 160, 171, 174, 176, 180, 192, 196, 197, 205, 206 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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) = 2 and a(2) = 13.
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
Sequence in context: A191765 A063615 A297837 * A262688 A020585 A038943
KEYWORD
nonn,easy,base
AUTHOR
Clark Kimberling, Sep 17 2014
STATUS
approved

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Last modified July 14 22:52 EDT 2024. Contains 374323 sequences. (Running on oeis4.)