A293762 Numbers k such that (d(k), d(k+1)) = (0,1) in the base-2 digits d(i) of sqrt(2).

2, 5, 7, 13, 16, 22, 26, 30, 39, 43, 49, 53, 56, 61, 65, 67, 71, 73, 79, 84, 87, 90, 94, 97, 101, 103, 105, 108, 110, 112, 114, 120, 123, 131, 135, 137, 140, 145, 152, 154, 158, 160, 164, 167, 170, 174, 178, 180, 185, 188, 192, 196, 199, 203, 205, 210, 212

Offset

1,1

Comments

This sequence together with A293761, 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 (0,1) first occurs as (a(2),a(3)).

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 *)

Crossrefs

Cf. A004539, A293761, A293763, A293764.

Sequence in context: A186131 A284191 A065897 * A161889 A275284 A261123

Adjacent sequences: A293759 A293760 A293761 * A293763 A293764 A293765

Keyword

nonn,easy,base

Author

Clark Kimberling, Oct 19 2017

Status

approved