A293728 - OEIS

%I #8 Apr 21 2021 03:50:34

%S 11,12,13,14,15,16,17,18,19,21,22,23,25,26,27,29,30,31,335,609,610,

%T 611,612,613,614,615,616,617,618,619,620,621,623,624,625,626,627,628,

%U 629,630,631,632,633,634,635,675,677,683,684,685,686,687,688,689,690

%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 base-2 expansion of sqrt(2).

%C This sequence together with A293725 and A293727 partition the nonnegative integers.

%H Clark Kimberling, <a href="/A293728/b293728.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 1,1

%A _Clark Kimberling_, Oct 18 2017