A293760 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 e.

2, 4, 32, 34, 36, 44, 46, 52, 54, 56, 58, 60, 62, 64, 66, 68, 96, 104, 108, 114, 226, 228, 230, 252, 254, 270, 296556, 296558, 296560, 296562, 296564, 296574, 296578, 296580, 296584, 296608, 296610, 296612, 296616, 297222, 297226, 297266, 297344, 297346

Offset

1,1

Comments

The greatest term in the b-file is a(7129) = 21896286 and there are no further terms up to 100 million binary digits of e. - Harvey P. Dale, Aug 07 2019

Links

Harvey P. Dale, Table of n, a(n) for n = 1..7129 (terms < 10^8; first 1489 terms from Robert Price)

Example

In base 2, e = 10.10110111111000010..., in which the initial segments of lengths 2 and 4 each have the same number of 0's and 1's.

Mathematica

z = 300; u = N[E, 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}]
Select[Range[z], c[0, #] == c[1, #] &]  (* A293760 *)
Position[Accumulate[RealDigits[E, 2, 300000][[1]]/.(0->-1)], 0]//Flatten (* Harvey P. Dale, Aug 07 2019 *)

Crossrefs

Cf. A004593, A029624.

Sequence in context: A019542 A319223 A299783 * A101575 A197099 A009098

Adjacent sequences: A293757 A293758 A293759 * A293761 A293762 A293763

Keyword

nonn,easy,base

Author

Clark Kimberling, Oct 18 2017

Extensions

a(27)-a(44) from Robert Price, Oct 19 2017

Status

approved