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).

2, 10, 20, 24, 28, 32, 318, 328, 330, 334, 336, 608, 622, 636, 638, 674, 676, 678, 680, 682, 826, 828, 832, 836, 838, 842, 844, 846, 848, 850, 852, 856, 858, 876, 880, 884, 886, 898, 906, 908, 918, 920, 928, 930, 942, 944, 946, 948, 950, 962, 964, 966, 968

Offset: 1

Author

Clark Kimberling, Oct 16 2017

Keywords

• nonn
• easy
• base

Comments

This sequence together with A293727 and A293728 partition the positive integers.

Examples

			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.
		

Crossrefs

Cf. A004539, A002103, A293726, A293727, A293728.

Programs

Mathematica

z = 300; u = N[Sqrt[2], z]; d = RealDigits[u, 2][[1]];
t[n_] := Take[d, n]; c[0, n_] := Count[t[n], 0]; c[1, n_] := Count[t[n], 1];
Table[{n, c[0, n], c[1, n]}, {n, 1, 100}]
u = Select[-1 + Range[z], c[0, #] == c[1, #] &]  (* A293725 *)
u/2  (* A293726 *)
Select[-1 + Range[z], c[0, #] < c[1, #] &]  (* A293727 *)
Select[-1 + Range[z], c[0, #] > c[1, #] &]  (* A293728 *)