A293788 Numbers k such that (d(k), d(k+1)) = (0,1) in the base-2 digits d(i) of sqrt(3).

3, 7, 10, 14, 19, 21, 25, 30, 32, 38, 41, 45, 47, 49, 51, 54, 59, 63, 67, 70, 72, 74, 78, 83, 85, 88, 90, 98, 105, 107, 115, 119, 125, 128, 131, 134, 136, 140, 147, 150, 153, 157, 162, 164, 167, 172, 175, 178, 182, 188, 193, 198, 203, 209, 211, 214, 218, 221

Offset

1,1

Comments

This sequence together with A293787, 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 (0,1) first occurs as (a(3),a(4)).

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

Cf. A004547, A293787, A293789, A293790.

Sequence in context: A184812 A140487 A310189 * A319480 A310190 A307203

Adjacent sequences: A293785 A293786 A293787 * A293789 A293790 A293791

Keyword

nonn,easy,base

Author

Clark Kimberling, Oct 19 2017

Status

approved