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A293787 Numbers k such that (d(k), d(k+1)) = (0,0) in the base-2 digits d(i) of sqrt(3). 4
13, 27, 28, 29, 35, 36, 37, 40, 44, 53, 58, 66, 69, 80, 81, 82, 94, 95, 96, 97, 103, 104, 111, 112, 113, 114, 123, 124, 127, 130, 133, 143, 144, 145, 146, 152, 156, 160, 161, 166, 177, 180, 181, 187, 191, 192, 196, 197, 202, 205, 206, 207, 208, 213, 217, 220 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
This sequence together with A293788, A293789, and A293790 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 (0,0) first occurs as (a(13),a(14)).
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 *)
SequencePosition[RealDigits[Sqrt[3], 2, 300][[1]], {0, 0}][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 30 2018 *)
CROSSREFS
Sequence in context: A033897 A005029 A251149 * A041330 A041765 A041328
KEYWORD
nonn,easy,base
AUTHOR
Clark Kimberling, Oct 19 2017
STATUS
approved

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Last modified April 23 15:20 EDT 2024. Contains 371916 sequences. (Running on oeis4.)