A293763 Numbers k such that (d(k), d(k+1)) = (1,0) in the base-2 digits d(i) of sqrt(2).

1, 4, 6, 8, 14, 20, 24, 28, 37, 42, 47, 51, 54, 57, 62, 66, 69, 72, 78, 81, 85, 89, 92, 96, 100, 102, 104, 106, 109, 111, 113, 119, 121, 128, 134, 136, 139, 144, 147, 153, 157, 159, 161, 165, 168, 173, 177, 179, 181, 186, 190, 195, 198, 200, 204, 209, 211

Offset

1,2

Comments

This sequence together with A293761, A293762, 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 (0,1) first occurs as (a(1),a(2)).

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, 250][[1]], {1, 0}][[;; , 1]] (* Harvey P. Dale, Dec 10 2023 *)

Crossrefs

Cf. A004539, A293761, A293762, A293764.

Sequence in context: A200077 A256137 A116897 * A246324 A280227 A181978

Adjacent sequences: A293760 A293761 A293762 * A293764 A293765 A293766

Keyword

nonn,easy,base

Author

Clark Kimberling, Oct 19 2017

Status

approved