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Numbers k such that (d(k), d(k+1)) = (1,1) in the base-2 digits d(i) of Pi.
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%I #6 Oct 20 2017 18:50:04

%S 1,13,14,15,16,17,20,42,49,59,65,73,78,82,95,96,105,108,109,116,117,

%T 121,149,150,170,174,175,176,177,181,186,187,207,208,211,212,213,214,

%U 222,227,228,231,239,240,244,247,282,283,284,288,293,294,299,313,316

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

%C This sequence, together with A293828, A293829, and A293830, partitions the positive integers.

%H Clark Kimberling, <a href="/A293831/b293831.txt">Table of n, a(n) for n = 1..10000</a>

%e (d(i)) = (1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0,...) = A004601, in which (1,1) first occurs as (a(1),a(2)).

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

%t Take[Map[#[[1]]&,StringPosition[s,"00"]],z] (*A293828*)

%t Take[Map[#[[1]]&,StringPosition[s,"01"]],z] (*A293829*)

%t Take[Map[#[[1]]&,StringPosition[s,"10"]],z] (*A293830*)

%t Take[Map[#[[1]]&,StringPosition[s,"11"]],z] (*A293831*)

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

%Y Cf. A004601, A293828, A293829, A293830.

%K nonn,easy,base

%O 1,2

%A _Clark Kimberling_, Oct 20 2017