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 A293763 Numbers k such that (d(k), d(k+1)) = (1,0) in the base-2 digits d(i) of sqrt(2). 4
 1, 4, 6, 8, 14, 20, 24, 28, 37, 42, 47, 51, 54, 57, 62, 66, 69, 72, 78, 81, 85, 89, 92, 96, 100, 102, 104, 106, 109, 111, 113, 119, 121, 128, 134, 136, 139, 144, 147, 153, 157, 159, 161, 165, 168, 173, 177, 179, 181, 186, 190, 195, 198, 200, 204, 209, 211 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This sequence together with A293761, A293762, and A293764 partition the positive integers. LINKS Clark Kimberling, Table of n, a(n) for n = 1..10000 EXAMPLE (d(i)) = (1,0,1,1,0,1,0,1,0,0,0,0,0,1,...) = A004539, in which (0,1) first occurs as (a(1),a(2)). MATHEMATICA z = 100; s = StringJoin[Map[ToString, First[RealDigits[N[Sqrt[2], 10000], 2]]]]; Take[Map[#[[1]]&, StringPosition[s, "00"]], z] (*A293761*) Take[Map[#[[1]]&, StringPosition[s, "01"]], z] (*A293762*) Take[Map[#[[1]]&, StringPosition[s, "10"]], z] (*A293763*) Take[Map[#[[1]]&, StringPosition[s, "11"]], z] (*A293764*) (* Peter J. C. Moses, Oct 15 2017 *) CROSSREFS Cf. A004539, A293761, A293762, A293764. Sequence in context: A200077 A256137 A116897 * A246324 A280227 A181978 Adjacent sequences: A293760 A293761 A293762 * A293764 A293765 A293766 KEYWORD nonn,easy,base AUTHOR Clark Kimberling, Oct 19 2017 STATUS approved

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Last modified December 5 23:11 EST 2023. Contains 367594 sequences. (Running on oeis4.)