A293728 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).

11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 335, 609, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 620, 621, 623, 624, 625, 626, 627, 628, 629, 630, 631, 632, 633, 634, 635, 675, 677, 683, 684, 685, 686, 687, 688, 689, 690

Offset: 1

Author

Clark Kimberling, Oct 18 2017

Keywords

• nonn
• easy
• base

Comments

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

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000

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[Range[z], c[0, #] == c[1, #] &]  (* A293725 *)
u/2  (* A293726 *)
Select[Range[z], c[0, #] < c[1, #] &]  (* A293727 *)
Select[Range[z], c[0, #] > c[1, #] &]  (* A293728 *)