

A293760


Numbers n such that c(n,0) = c(n,1), where c(n,d) = number of d's in the first n digits of the base2 expansion of e.


1



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
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OFFSET

1,1


COMMENTS

The greatest term in the bfile 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 (* First 1489 terms from Robert Price  see comment *)


EXAMPLE

In base2, 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



