cp's OEIS Frontend

A293725 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).

%I A293725 #15 Apr 21 2021 04:26:19
%S A293725 2,10,20,24,28,32,318,328,330,334,336,608,622,636,638,674,676,678,680,
%T A293725 682,826,828,832,836,838,842,844,846,848,850,852,856,858,876,880,884,
%U A293725 886,898,906,908,918,920,928,930,942,944,946,948,950,962,964,966,968
%N A293725 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 A293725 This sequence together with A293727 and A293728 partition the positive integers.
%e A293725 In base 2, sqrt(2) = 1.0110101000001001111001..., so that initial segments 1.0; 1.011010100..., of lengths 2,10,... have the same number of 0's and 1's.
%t A293725 z = 300; u = N[Sqrt[2], z]; d = RealDigits[u, 2][[1]];
%t A293725 t[n_] := Take[d, n]; c[0, n_] := Count[t[n], 0]; c[1, n_] := Count[t[n], 1];
%t A293725 Table[{n, c[0, n], c[1, n]}, {n, 1, 100}]
%t A293725 u = Select[-1 + Range[z], c[0, #] == c[1, #] &]  (* A293725 *)
%t A293725 u/2  (* A293726 *)
%t A293725 Select[-1 + Range[z], c[0, #] < c[1, #] &]  (* A293727 *)
%t A293725 Select[-1 + Range[z], c[0, #] > c[1, #] &]  (* A293728 *)
%Y A293725 Cf. A004539, A002103, A293726, A293727, A293728.
%K A293725 nonn,easy,base
%O A293725 1,1
%A A293725 _Clark Kimberling_, Oct 16 2017