A293762 - OEIS

%I #6 Oct 19 2017 22:40:39

%S 2,5,7,13,16,22,26,30,39,43,49,53,56,61,65,67,71,73,79,84,87,90,94,97,

%T 101,103,105,108,110,112,114,120,123,131,135,137,140,145,152,154,158,

%U 160,164,167,170,174,178,180,185,188,192,196,199,203,205,210,212

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

%C This sequence together with A293761, A293763, and A293764 partition the positive integers.

%H Clark Kimberling, <a href="/A293762/b293762.txt">Table of n, a(n) for n = 1..10000</a>

%e (d(i)) = (1,0,1,1,0,1,0,1,0,0,0,0,0,1,...) = A004539, in which (0,1) first occurs as (a(2),a(3)).

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

%t Take[Map[#[[1]]&,StringPosition[s,"00"]],z] (*A293761*)

%t Take[Map[#[[1]]&,StringPosition[s,"01"]],z] (*A293762*)

%t Take[Map[#[[1]]&,StringPosition[s,"10"]],z] (*A293763*)

%t Take[Map[#[[1]]&,StringPosition[s,"11"]],z] (*A293764*)

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

%Y Cf. A004539, A293761, A293763, A293764.

%K nonn,easy,base

%O 1,1

%A _Clark Kimberling_, Oct 19 2017