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%I #8 Dec 10 2023 17:12:20
%S 1,4,6,8,14,20,24,28,37,42,47,51,54,57,62,66,69,72,78,81,85,89,92,96,
%T 100,102,104,106,109,111,113,119,121,128,134,136,139,144,147,153,157,
%U 159,161,165,168,173,177,179,181,186,190,195,198,200,204,209,211
%N Numbers k such that (d(k), d(k+1)) = (1,0) in the base-2 digits d(i) of sqrt(2).
%C This sequence together with A293761, A293762, and A293764 partition the positive integers.
%H Clark Kimberling, <a href="/A293763/b293763.txt">Table of n, a(n) for n = 1..10000</a>
%e (d(i)) = (1,0,1,1,0,1,0,1,0,0,0,0,0,1,...) = A004539, in which (0,1) first occurs as (a(1),a(2)).
%t z = 100; s = StringJoin[Map[ToString, First[RealDigits[N[Sqrt[2], 10000], 2]]]];
%t Take[Map[#[[1]]&,StringPosition[s,"00"]],z] (*A293761*)
%t Take[Map[#[[1]]&,StringPosition[s,"01"]],z] (*A293762*)
%t Take[Map[#[[1]]&,StringPosition[s,"10"]],z] (*A293763*)
%t Take[Map[#[[1]]&,StringPosition[s,"11"]],z] (*A293764*)
%t (* _Peter J. C. Moses_, Oct 15 2017 *)
%t SequencePosition[RealDigits[Sqrt[2],2,250][[1]],{1,0}][[;;,1]] (* _Harvey P. Dale_, Dec 10 2023 *)
%Y Cf. A004539, A293761, A293762, A293764.
%K nonn,easy,base
%O 1,2
%A _Clark Kimberling_, Oct 19 2017
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