A293792 - OEIS

%I #9 Jan 24 2021 12:43:42

%S 14,15,16,23,24,30,31,36,37,51,58,79,80,88,89,92,93,94,95,96,97,100,

%T 105,113,119,125,126,134,135,142,147,148,154,155,156,157,163,168,169,

%U 177,186,198,204,205,206,209,216,219,220,221,222,225,226,231,232,236

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

%C This sequence together with A293793, A293794, and A293795 partition the positive integers.

%H Clark Kimberling, <a href="/A293792/b293792.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 (0,0) first occurs as (a(14),a(15)).

%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]],{0,0}][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jan 24 2021 *)

%Y Cf. A004593, A293793, A293794, A293795.

%K nonn,easy,base

%O 1,1

%A _Clark Kimberling_, Oct 19 2017