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%I #8 Apr 21 2021 03:49:27
%S 1,3,4,5,6,7,8,9,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,
%T 50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,
%U 73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91
%N Numbers k such that c(k,0) < c(k,1), where c(k,d) = number of d's in the first k digits of the base-2 expansion of sqrt(2).
%C This sequence together with A293725 and A293728 partition the nonnegative integers.
%H Clark Kimberling, <a href="/A293727/b293727.txt">Table of n, a(n) for n = 1..10000</a>
%t z = 300; u = N[Sqrt[2], z]; d = RealDigits[u, 2][[1]];
%t t[n_] := Take[d, n]; c[0, n_] := Count[t[n], 0]; c[1, n_] := Count[t[n], 1];
%t Table[{n, c[0, n], c[1, n]}, {n, 1, 100}]
%t u = Select[Range[z], c[0, #] == c[1, #] &] (* A293725 *)
%t u/2 (* A293726 *)
%t Select[Range[z], c[0, #] < c[1, #] &] (* A293727 *)
%t Select[Range[z], c[0, #] > c[1, #] &] (* A293728 *)
%Y Cf. A004539, A002103, A293726, A293727, A293728.
%K nonn,easy,base
%O 1,2
%A _Clark Kimberling_, Oct 18 2017