A293831 Numbers k such that (d(k), d(k+1)) = (1,1) in the base-2 digits d(i) of Pi.

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

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