A293761 Numbers k such that (d(k), d(k+1)) = (0,0) in the base-2 digits d(i) of sqrt(2).

9, 10, 11, 12, 15, 21, 25, 29, 38, 48, 52, 55, 58, 59, 60, 63, 64, 70, 82, 83, 86, 93, 107, 122, 129, 130, 148, 149, 150, 151, 162, 163, 166, 169, 182, 183, 184, 187, 191, 201, 202, 215, 218, 219, 220, 226, 227, 228, 229, 233, 237, 242, 246, 249, 250, 259

Offset

1,1

Comments

This sequence together with A293762, A293763, and A293764 partition the positive integers.

Links

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

Example

(d(i)) = (1,0,1,1,0,1,0,1,0,0,0,0,0,1,...) = A004539, in which (0,0) first occurs as (a(9),a(10)).

Mathematica

z = 100; s = StringJoin[Map[ToString, First[RealDigits[N[Sqrt[2], 10000], 2]]]];
Take[Map[#[[1]]&, StringPosition[s, "00"]], z] (*A293761*)
Take[Map[#[[1]]&, StringPosition[s, "01"]], z] (*A293762*)
Take[Map[#[[1]]&, StringPosition[s, "10"]], z] (*A293763*)
Take[Map[#[[1]]&, StringPosition[s, "11"]], z] (*A293764*)
(* Peter J. C. Moses, Oct 15 2017 *)
SequencePosition[RealDigits[Sqrt[2], 2, 300][[1]], {0, 0}][[All, 1]] (* Harvey P. Dale, Jan 18 2023 *)

Crossrefs

Cf. A004539, A293762, A293763, A293764.

Sequence in context: A360538 A173147 A342145 * A253881 A097480 A034068

Adjacent sequences: A293758 A293759 A293760 * A293762 A293763 A293764

Keyword

nonn,easy,base

Author

Clark Kimberling, Oct 19 2017

Status

approved