A293828 - OEIS

A293828

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

3, 6, 9, 10, 11, 28, 29, 32, 33, 36, 37, 38, 46, 47, 51, 52, 53, 56, 57, 63, 67, 68, 71, 75, 76, 80, 84, 85, 90, 91, 98, 99, 100, 101, 102, 103, 111, 112, 113, 114, 119, 125, 126, 129, 134, 137, 138, 139, 140, 141, 144, 147, 152, 153, 154, 155, 158, 159, 162

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

This sequence, together with A293829, A293830, 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 (0,0) first occurs as (a(3),a(4)).

MATHEMATICA

z = 100; s = StringJoin[Map[ToString, First[RealDigits[N[Pi], 10000], 2]]]];

Take[Map[#[[1]]&, StringPosition[s, "00"]], z] (*A293828*)