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
Examples
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.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..7129 (terms < 10^8; first 1489 terms from Robert Price)
Programs
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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 *)
Extensions
a(27)-a(44) from Robert Price, Oct 19 2017
Comments