A293755 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 tau (the golden ratio, (1+sqrt(5))/2).

143, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 157, 159, 223, 224, 225, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265

Offset

1,1

Comments

This sequence together with A293752 and A293754 partition the positive integers.

Links

Table of n, a(n) for n=1..52.

Mathematica

z = 300; u = N[GoldenRatio, 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, #] &]  (* A293752 *)
u/2  (* A293753 *)
Select[Range[z], c[0, #] < c[1, #] &]  (* A293754 *)
Select[Range[z], c[0, #] > c[1, #] &]  (* A293755 *)

Crossrefs

Cf. A068432, A293752, A293753, A293754.

Sequence in context: A217142 A306090 A296887 * A160781 A217141 A097435

Adjacent sequences: A293752 A293753 A293754 * A293756 A293757 A293758

Keyword

nonn,easy,base

Author

Clark Kimberling, Oct 18 2017

Status

approved