A293752 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 phi (the golden ratio, (1+sqrt(5))/2).

4, 142, 144, 156, 158, 160, 192, 220, 222, 226, 228, 230, 276, 278, 310, 312, 314, 334, 340, 358, 360, 374, 376, 380, 390, 394, 628, 662, 664, 672, 678, 680, 682, 684, 686, 692, 694, 700, 718, 720, 722, 740, 1666, 1670, 1674, 1688, 1690, 1692, 1698, 1724

Offset

1,1

Comments

This sequence together with A293754 and A293755 partition the positive integers.

Links

Table of n, a(n) for n=1..50.

Example

In base 2, phi = 1.10011110001101110111100..., so that the initial segment
1.100, of length 4 is the first segment to have the same number of 0's and 1's, so that a(1) = 4.

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, A293753, A293754, A293755.

Sequence in context: A299722 A210831 A247483 * A299833 A231949 A239248

Adjacent sequences: A293749 A293750 A293751 * A293753 A293754 A293755

Keyword

nonn,easy,base

Author

Clark Kimberling, Oct 18 2017

Status

approved