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A247634
Numbers k such that d(r,k) = 1 and d(s,k) = 1, where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {sqrt(8)}, and { } = fractional part.
4
2, 16, 17, 18, 22, 26, 30, 31, 32, 33, 34, 35, 39, 40, 43, 44, 45, 49, 67, 73, 74, 75, 76, 79, 87, 90, 94, 97, 98, 114, 115, 116, 117, 123, 124, 125, 126, 131, 132, 137, 140, 141, 142, 145, 154, 155, 170, 171, 174, 175, 188, 192, 193, 196, 205, 206, 207, 212
OFFSET
1,1
COMMENTS
Every positive integer lies in exactly one of these: A247631, A247632, A247633, A247634.
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) = 1 and a(2) = 4.
MATHEMATICA
z = 400; 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]]
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]] (* A247631 *)
Flatten[Position[t2, 1]] (* A247632 *)
Flatten[Position[t3, 1]] (* A247633 *)
Flatten[Position[t4, 1]] (* A247634 *)
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Clark Kimberling, Sep 23 2014
STATUS
approved