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 A247456 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 = {3*sqrt(2)}, and { } = fractional part. 4
 4, 6, 12, 14, 20, 24, 28, 37, 47, 52, 55, 60, 63, 69, 83, 85, 92, 100, 102, 104, 106, 119, 121, 129, 150, 157, 159, 163, 166, 168, 177, 179, 184, 186, 190, 198, 201, 215, 219, 228, 232, 236, 241, 246, 250, 252, 254, 256, 258, 271, 276, 284, 288, 303, 305 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Every positive integer lies in exactly one of these: A247455, A247456, A247457, A247458. LINKS Clark Kimberling, Table of n, a(n) for n = 1..500 EXAMPLE {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) = 4 and a(2) = 6. MATHEMATICA z = 400; 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]] 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]]  (* A247455 *) Flatten[Position[t2, 1]]  (* A247456 *) Flatten[Position[t3, 1]]  (* A247457 *) Flatten[Position[t4, 1]]  (* A247458 *) CROSSREFS Cf. A247455, A247457, A247458. Sequence in context: A047406 A136415 A310596 * A266383 A217948 A059891 Adjacent sequences:  A247453 A247454 A247455 * A247457 A247458 A247459 KEYWORD nonn,easy,base AUTHOR Clark Kimberling, Sep 18 2014 STATUS approved

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Last modified April 20 01:03 EDT 2021. Contains 343117 sequences. (Running on oeis4.)