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 A293829 Numbers k such that (d(k), d(k+1)) = (0,1) in the base-2 digits d(i) of Pi. 4

%I #6 Jan 18 2023 15:38:40

%S 4,7,12,19,22,24,26,30,34,39,41,44,48,54,58,61,64,69,72,77,81,86,88,

%T 92,94,104,107,115,120,123,127,130,132,135,142,145,148,156,160,164,

%U 166,169,173,180,185,189,198,204,206,210,216,218,221,226,230,235,238

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

%H Clark Kimberling, <a href="/A293829/b293829.txt">Table of n, a(n) for n = 1..10000</a>

%e This sequence together with A293828, A293830, and A293831 partition the positive integers.

%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 (0,1) 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 *)

%t SequencePosition[RealDigits[Pi,2,300][[1]],{0,1}][[All,1]] (* _Harvey P. Dale_, Jan 18 2023 *)

%Y Cf. A004601, A293828, A293830, A293831.

%K nonn,easy,base

%O 1,1

%A _Clark Kimberling_, Oct 20 2017

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Last modified March 3 04:18 EST 2024. Contains 370499 sequences. (Running on oeis4.)