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A293830 Numbers k such that (d(k), d(k+1)) = (1,0) in the base-2 digits d(i) of Pi. 4

%I

%S 2,5,8,18,21,23,25,27,31,35,40,43,45,50,55,60,62,66,70,74,79,83,87,89,

%T 93,97,106,110,118,122,124,128,131,133,136,143,146,151,157,161,165,

%U 167,171,178,182,188,190,199,205,209,215,217,219,223,229,232,236

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

%C This sequence, together with A293828, A293829, and A293831, partitions the positive integers.

%H Clark Kimberling, <a href="/A293830/b293830.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 (1,0) first occurs as (a(4),a(5)).

%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, A293831.

%K nonn,easy,base

%O 1,1

%A _Clark Kimberling_, Oct 20 2017

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Last modified April 3 15:51 EDT 2020. Contains 333197 sequences. (Running on oeis4.)