A293727 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).

1, 3, 4, 5, 6, 7, 8, 9, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91

Offset

1,2

Comments

This sequence together with A293725 and A293728 partition the nonnegative integers.

Links

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

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 *)

Crossrefs

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

Sequence in context: A097389 A051415 A037351 * A077528 A329254 A359003

Adjacent sequences: A293724 A293725 A293726 * A293728 A293729 A293730

Keyword

nonn,easy,base

Author

Clark Kimberling, Oct 18 2017

Status

approved