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%I #9 Jan 18 2023 13:00:12
%S 9,10,11,12,15,21,25,29,38,48,52,55,58,59,60,63,64,70,82,83,86,93,107,
%T 122,129,130,148,149,150,151,162,163,166,169,182,183,184,187,191,201,
%U 202,215,218,219,220,226,227,228,229,233,237,242,246,249,250,259
%N Numbers k such that (d(k), d(k+1)) = (0,0) in the base-2 digits d(i) of sqrt(2).
%C This sequence together with A293762, A293763, and A293764 partition the positive integers.
%H Clark Kimberling, <a href="/A293761/b293761.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 (0,0) first occurs as (a(9),a(10)).
%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],2,300][[1]],{0,0}][[All,1]] (* _Harvey P. Dale_, Jan 18 2023 *)
%Y Cf. A004539, A293762, A293763, A293764.
%K nonn,easy,base
%O 1,1
%A _Clark Kimberling_, Oct 19 2017
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