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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.

%I A293760 #28 Nov 06 2023 02:59:48
%S A293760 2,4,32,34,36,44,46,52,54,56,58,60,62,64,66,68,96,104,108,114,226,228,
%T A293760 230,252,254,270,296556,296558,296560,296562,296564,296574,296578,
%U A293760 296580,296584,296608,296610,296612,296616,297222,297226,297266,297344,297346
%N 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.
%C A293760 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
%H A293760 Harvey P. Dale, <a href="/A293760/b293760.txt">Table of n, a(n) for n = 1..7129</a> (terms < 10^8; first 1489 terms from Robert Price)
%e A293760 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.
%t A293760 z = 300; u = N[E, z]; d = RealDigits[u, 2][[1]];
%t A293760 t[n_] := Take[d, n]; c[0, n_] := Count[t[n], 0]; c[1, n_] := Count[t[n], 1];
%t A293760 Table[{n, c[0, n], c[1, n]}, {n, 1, 100}]
%t A293760 Select[Range[z], c[0, #] == c[1, #] &]  (* A293760 *)
%t A293760 Position[Accumulate[RealDigits[E,2,300000][[1]]/.(0->-1)],0]//Flatten (* _Harvey P. Dale_, Aug 07 2019 *)
%Y A293760 Cf. A004593, A029624.
%K A293760 nonn,easy,base
%O A293760 1,1
%A A293760 _Clark Kimberling_, Oct 18 2017
%E A293760 a(27)-a(44) from _Robert Price_, Oct 19 2017