A293831 - OEIS

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

(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*)