A293787 - OEIS

%I #9 Jan 30 2018 17:36:28

%S 13,27,28,29,35,36,37,40,44,53,58,66,69,80,81,82,94,95,96,97,103,104,

%T 111,112,113,114,123,124,127,130,133,143,144,145,146,152,156,160,161,

%U 166,177,180,181,187,191,192,196,197,202,205,206,207,208,213,217,220

%N Numbers k such that (d(k), d(k+1)) = (0,0) in the base-2 digits d(i) of sqrt(3).

%C This sequence together with A293788, A293789, and A293790 partition the positive integers.

%H Clark Kimberling, <a href="/A293787/b293787.txt">Table of n, a(n) for n = 1..10000</a>

%e (d(i)) = (1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0,...) = A004547, in which (0,0) first occurs as (a(13),a(14)).

%t z = 100; s = StringJoin[Map[ToString, First[RealDigits[N[Sqrt[3], 10000], 2]]]];

%t Take[Map[#[[1]]&,StringPosition[s,"00"]],z] (*A293787*)

%t Take[Map[#[[1]]&,StringPosition[s,"01"]],z] (*A293788*)

%t Take[Map[#[[1]]&,StringPosition[s,"10"]],z] (*A293789*)

%t Take[Map[#[[1]]&,StringPosition[s,"11"]],z] (*A293790*)

%t (* _Peter J. C. Moses_, Oct 15 2017 *)

%t SequencePosition[RealDigits[Sqrt[3],2,300][[1]],{0,0}][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jan 30 2018 *)

%Y Cf. A004547, A293788, A293789, A293790.

%K nonn,easy,base

%O 1,1

%A _Clark Kimberling_, Oct 19 2017