

A293764


Numbers k such that (d(k), d(k+1)) = (1,1) in the base2 digits d(i) of sqrt(2).


4



3, 17, 18, 19, 23, 27, 31, 32, 33, 34, 35, 36, 40, 41, 44, 45, 46, 50, 68, 74, 75, 76, 77, 80, 88, 91, 95, 98, 99, 115, 116, 117, 118, 124, 125, 126, 127, 132, 133, 138, 141, 142, 143, 146, 155, 156, 171, 172, 175, 176, 189, 193, 194, 197, 206, 207, 208, 213
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OFFSET

1,1


COMMENTS

This sequence together with A293761, A293762, and A293763 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(3),a(4)).


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, A293762, A293763.
Sequence in context: A195999 A059189 A043066 * A295395 A246143 A101144
Adjacent sequences: A293761 A293762 A293763 * A293765 A293766 A293767


KEYWORD

nonn,easy,base


AUTHOR

Clark Kimberling, Oct 19 2017


STATUS

approved



