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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

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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*)