A293754 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).

1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 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

Offset

1,2

Comments

This sequence together with A293752 and A293755 partition the positive integers.

Links

Table of n, a(n) for n=1..67.

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, A293755.

Sequence in context: A031976 A023839 A004723 * A242410 A258022 A333638

Adjacent sequences: A293751 A293752 A293753 * A293755 A293756 A293757

Keyword

nonn,easy,base

Author

Clark Kimberling, Oct 18 2017

Status

approved