A293790 - OEIS

A293790

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

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

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 (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*)