A293830 Numbers k such that (d(k), d(k+1)) = (1,0) in the base-2 digits d(i) of Pi.

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

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: A343129 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