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A293831
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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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4
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1, 13, 14, 15, 16, 17, 20, 42, 49, 59, 65, 73, 78, 82, 95, 96, 105, 108, 109, 116, 117, 121, 149, 150, 170, 174, 175, 176, 177, 181, 186, 187, 207, 208, 211, 212, 213, 214, 222, 227, 228, 231, 239, 240, 244, 247, 282, 283, 284, 288, 293, 294, 299, 313, 316
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OFFSET
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1,2
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COMMENTS
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This sequence, together with A293828, A293829, and A293830, partitions the positive integers.
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LINKS
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Clark Kimberling, Table of n, a(n) for n = 1..10000
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EXAMPLE
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(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)).
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MATHEMATICA
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z = 100; s = StringJoin[Map[ToString, First[RealDigits[N[Pi], 10000], 2]]]];
Take[Map[#[[1]]&, StringPosition[s, "00"]], z] (*A293828*)
Take[Map[#[[1]]&, StringPosition[s, "01"]], z] (*A293829*)
Take[Map[#[[1]]&, StringPosition[s, "10"]], z] (*A293830*)
Take[Map[#[[1]]&, StringPosition[s, "11"]], z] (*A293831*)
(* Peter J. C. Moses, Oct 15 2017 *)
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CROSSREFS
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Cf. A004601, A293828, A293829, A293830.
Sequence in context: A178402 A132580 A138596 * A118140 A108854 A106007
Adjacent sequences: A293828 A293829 A293830 * A293832 A293833 A293834
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KEYWORD
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nonn,easy,base
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AUTHOR
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Clark Kimberling, Oct 20 2017
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STATUS
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approved
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