A293793 - OEIS

%I #8 Apr 09 2022 12:00:38

%S 2,4,7,17,19,21,25,27,32,34,38,40,42,46,49,52,54,56,59,62,64,66,68,75,

%T 81,83,85,90,98,101,106,111,114,120,127,131,136,138,143,149,151,158,

%U 164,170,172,175,178,181,184,187,189,191,194,196,199,207,210,213

%N Numbers k such that (d(k), d(k+1)) = (0,1) in the base-2 digits d(i) of e.

%C A293792, A293794, and A293795 partition the positive integers.

%H Clark Kimberling, <a href="/A293793/b293793.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 (0,1) first occurs as (a(2),a(3)).

%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,2,300][[1]],{0,1}][[All,1]] (* _Harvey P. Dale_, Apr 09 2022 *)

%Y Cf. A004593, A293792, A293794, A293795.

%K nonn,easy,base

%O 1,1

%A _Clark Kimberling_, Oct 19 2017