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A293831 Numbers k such that (d(k), d(k+1)) = (1,1) in the base-2 digits d(i) of Pi. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000

EXAMPLE

(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)).

MATHEMATICA

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 *)

CROSSREFS

Cf. A004601, A293828, A293829, A293830.

Sequence in context: A178402 A132580 A138596 * A118140 A108854 A106007

Adjacent sequences:  A293828 A293829 A293830 * A293832 A293833 A293834

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Oct 20 2017

STATUS

approved

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Last modified April 7 04:20 EDT 2020. Contains 333292 sequences. (Running on oeis4.)