A293787 Numbers k such that (d(k), d(k+1)) = (0,0) in the base-2 digits d(i) of sqrt(3).

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

Offset

1,1

Comments

This sequence together with A293788, A293789, and A293790 partition the positive integers.

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

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

Cf. A004547, A293788, A293789, A293790.

Sequence in context: A033897 A005029 A251149 * A041330 A041765 A041328

Adjacent sequences: A293784 A293785 A293786 * A293788 A293789 A293790

Keyword

nonn,easy,base

Author

Clark Kimberling, Oct 19 2017

Status

approved