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%I #6 Oct 19 2017 22:41:28
%S 1,4,5,8,11,15,16,17,22,23,33,42,55,56,60,61,64,75,76,86,91,92,99,100,
%T 101,108,109,116,117,120,121,137,138,141,148,154,158,168,169,170,173,
%U 183,184,185,189,194,199,200,215,227,230,231,241,247,250,251,272
%N Numbers k such that (d(k), d(k+1)) = (1,1) in the base-2 digits d(i) of sqrt(3).
%C This sequence together with A293787, A293788, and A293789 partition the positive integers.
%H Clark Kimberling, <a href="/A293790/b293790.txt">Table of n, a(n) for n = 1..10000</a>
%e (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)).
%t z = 100; s = StringJoin[Map[ToString, First[RealDigits[N[Sqrt[3], 10000], 2]]]];
%t Take[Map[#[[1]]&,StringPosition[s,"00"]],z] (*A293787*)
%t Take[Map[#[[1]]&,StringPosition[s,"01"]],z] (*A293788*)
%t Take[Map[#[[1]]&,StringPosition[s,"10"]],z] (*A293789*)
%t Take[Map[#[[1]]&,StringPosition[s,"11"]],z] (*A293790*)
%t (* _Peter J. C. Moses_, Oct 15 2017 *)
%Y Cf. A004547, A293787, A293788, A293789.
%K nonn,easy,base
%O 1,2
%A _Clark Kimberling_, Oct 19 2017
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