A293788 - OEIS

%I #8 Sep 09 2024 18:54:30

%S 3,7,10,14,19,21,25,30,32,38,41,45,47,49,51,54,59,63,67,70,72,74,78,

%T 83,85,88,90,98,105,107,115,119,125,128,131,134,136,140,147,150,153,

%U 157,162,164,167,172,175,178,182,188,193,198,203,209,211,214,218,221

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

%C This sequence together with A293787, A293789, and A293790 partition the positive integers.

%H Clark Kimberling, <a href="/A293788/b293788.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 (0,1) first occurs as (a(3),a(4)).

%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]],{0,1}][[;;,1]] (* _Harvey P. Dale_, Sep 09 2024 *)

%Y Cf. A004547, A293787, A293789, A293790.

%K nonn,easy,base

%O 1,1

%A _Clark Kimberling_, Oct 19 2017