%I #8 May 29 2019 15:41:42
%S 1,3,6,13,18,20,22,26,29,33,35,39,41,45,48,50,53,55,57,61,63,65,67,74,
%T 78,82,84,87,91,99,104,110,112,118,124,130,133,137,141,146,150,153,
%U 162,167,171,174,176,180,183,185,188,190,193,195,197,203,208,212
%N Numbers k such that (d(k), d(k+1)) = (1,0) in the base-2 digits d(i) of e.
%C This sequence, together with A293792, A293793 and A293795, partitions the positive integers.
%H Clark Kimberling, <a href="/A293794/b293794.txt">Table of n, a(n) for n = 1..10000</a>
%e (d(i)) = (1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1,...) = A004593, in which (1,0) first occurs as (a(1),a(2)).
%t z = 100; s = StringJoin[Map[ToString, First[RealDigits[N[E], 10000], 2]]]];
%t Take[Map[#[[1]]&,StringPosition[s,"00"]],z] (*A293792*)
%t Take[Map[#[[1]]&,StringPosition[s,"01"]],z] (*A293793*)
%t Take[Map[#[[1]]&,StringPosition[s,"10"]],z] (*A293794*)
%t Take[Map[#[[1]]&,StringPosition[s,"11"]],z] (*A293795*)
%t (* _Peter J. C. Moses_, Oct 15 2017 *)
%t SequencePosition[RealDigits[E,2,250][[1]],{1,0}][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, May 29 2019 *)
%Y Cf. A004593, A293792, A293793, A293795.
%K nonn,easy,base
%O 1,2
%A _Clark Kimberling_, Oct 20 2017