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

1,1

Comments

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

Links

Table of n, a(n) for n=1..53.

Example

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.

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 *)

Crossrefs

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

Sequence in context: A306105 A038103 A307254 * A351552 A305448 A177150

Adjacent sequences: A293722 A293723 A293724 * A293726 A293727 A293728

Keyword

nonn,easy,base

Author

Clark Kimberling, Oct 16 2017

Status

approved