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

4, 7, 12, 19, 22, 24, 26, 30, 34, 39, 41, 44, 48, 54, 58, 61, 64, 69, 72, 77, 81, 86, 88, 92, 94, 104, 107, 115, 120, 123, 127, 130, 132, 135, 142, 145, 148, 156, 160, 164, 166, 169, 173, 180, 185, 189, 198, 204, 206, 210, 216, 218, 221, 226, 230, 235, 238

Offset

1,1

Links

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

Example

This sequence together with A293828, A293830, and A293831 partition the positive integers.
(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)).

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 *)
SequencePosition[RealDigits[Pi, 2, 300][[1]], {0, 1}][[All, 1]] (* Harvey P. Dale, Jan 18 2023 *)

Crossrefs

Cf. A004601, A293828, A293830, A293831.

Sequence in context: A132297 A007333 A097536 * A344421 A022809 A297554

Adjacent sequences: A293826 A293827 A293828 * A293830 A293831 A293832

Keyword

nonn,easy,base

Author

Clark Kimberling, Oct 20 2017

Status

approved