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A293761 Numbers k such that (d(k), d(k+1)) = (0,0) in the base-2 digits d(i) of sqrt(2). 4
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 (list; graph; refs; listen; history; text; internal format)
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 *)

CROSSREFS

Cf. A004539, A293762, A293763, A293764.

Sequence in context: A274562 A258469 A173147 * A253881 A097480 A034068

Adjacent sequences:  A293758 A293759 A293760 * A293762 A293763 A293764

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Oct 19 2017

STATUS

approved

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Last modified December 8 18:37 EST 2019. Contains 329865 sequences. (Running on oeis4.)