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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
2, 5, 8, 18, 21, 23, 25, 27, 31, 35, 40, 43, 45, 50, 55, 60, 62, 66, 70, 74, 79, 83, 87, 89, 93, 97, 106, 110, 118, 122, 124, 128, 131, 133, 136, 143, 146, 151, 157, 161, 165, 167, 171, 178, 182, 188, 190, 199, 205, 209, 215, 217, 219, 223, 229, 232, 236 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence, together with A293828, A293829, and A293831, 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 (1,0) first occurs as (a(4),a(5)).

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, A293831.

Sequence in context: A112361 A050872 A086324 * A073708 A024460 A039658

Adjacent sequences:  A293827 A293828 A293829 * A293831 A293832 A293833

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Oct 20 2017

STATUS

approved

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Last modified February 27 06:36 EST 2020. Contains 332299 sequences. (Running on oeis4.)