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A293762 Numbers k such that (d(k), d(k+1)) = (0,1) in the base-2 digits d(i) of sqrt(2). 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 6 14:15 EST 2019. Contains 329806 sequences. (Running on oeis4.)