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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Every positive integer lies in exactly one of the sequences A247635 and A247636. LINKS Clark Kimberling, Table of n, a(n) for n = 1..1000 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 Cf. A247636, A247631, A247523. Sequence in context: A081101 A043059 A237415 * A152754 A001560 A175463 Adjacent sequences:  A247632 A247633 A247634 * A247636 A247637 A247638 KEYWORD nonn,easy,base AUTHOR Clark Kimberling, Sep 23 2014 STATUS approved

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Last modified April 20 13:26 EDT 2021. Contains 343135 sequences. (Running on oeis4.)