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A247635
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(8)}, and { } = fractional part.
2
2, 8, 9, 10, 11, 14, 16, 17, 18, 20, 22, 24, 26, 28, 30, 31, 32, 33, 34, 35, 37, 39, 40, 43, 44, 45, 47, 49, 51, 54, 57, 58, 59, 62, 63, 67, 69, 73, 74, 75, 76, 79, 81, 82, 85, 87, 90, 92, 94, 97, 98, 106, 114, 115, 116, 117, 121, 123, 124, 125, 126, 128
OFFSET
1,1
COMMENTS
Every positive integer lies in exactly one of the sequences A247635 and A247636.
LINKS
EXAMPLE
r has binary digits 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, ...
s has binary digits 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, ...
so that a(1) = 2 and a(2) = 8.
MATHEMATICA
z = 200; r = FractionalPart[Sqrt[2]]; s = FractionalPart[Sqrt[8]];
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]] (* A247635 *)
Flatten[Position[t, 0]] (* A247636 *)
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Clark Kimberling, Sep 23 2014
STATUS
approved