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A293790 Numbers k such that (d(k), d(k+1)) = (1,1) in the base-2 digits d(i) of sqrt(3). 4
1, 4, 5, 8, 11, 15, 16, 17, 22, 23, 33, 42, 55, 56, 60, 61, 64, 75, 76, 86, 91, 92, 99, 100, 101, 108, 109, 116, 117, 120, 121, 137, 138, 141, 148, 154, 158, 168, 169, 170, 173, 183, 184, 185, 189, 194, 199, 200, 215, 227, 230, 231, 241, 247, 250, 251, 272 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
This sequence together with A293787, A293788, and A293789 partition the positive integers.
LINKS
EXAMPLE
(d(i)) = (1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0,...) = A004547, in which (1,1) first occurs as (a(1),a(2)).
MATHEMATICA
z = 100; s = StringJoin[Map[ToString, First[RealDigits[N[Sqrt[3], 10000], 2]]]];
Take[Map[#[[1]]&, StringPosition[s, "00"]], z] (*A293787*)
Take[Map[#[[1]]&, StringPosition[s, "01"]], z] (*A293788*)
Take[Map[#[[1]]&, StringPosition[s, "10"]], z] (*A293789*)
Take[Map[#[[1]]&, StringPosition[s, "11"]], z] (*A293790*)
(* Peter J. C. Moses, Oct 15 2017 *)
CROSSREFS
Sequence in context: A260989 A285566 A353044 * A190778 A117573 A354937
KEYWORD
nonn,easy,base
AUTHOR
Clark Kimberling, Oct 19 2017
STATUS
approved

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Last modified March 18 21:02 EDT 2024. Contains 370951 sequences. (Running on oeis4.)