A293794 Numbers k such that (d(k), d(k+1)) = (1,0) in the base-2 digits d(i) of e.

1, 3, 6, 13, 18, 20, 22, 26, 29, 33, 35, 39, 41, 45, 48, 50, 53, 55, 57, 61, 63, 65, 67, 74, 78, 82, 84, 87, 91, 99, 104, 110, 112, 118, 124, 130, 133, 137, 141, 146, 150, 153, 162, 167, 171, 174, 176, 180, 183, 185, 188, 190, 193, 195, 197, 203, 208, 212

Offset

1,2

Comments

This sequence, together with A293792, A293793 and A293795, partitions the positive integers.

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

Example

(d(i)) = (1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1,...) = A004593, in which (1,0) first occurs as (a(1),a(2)).

Mathematica

z = 100; s = StringJoin[Map[ToString, First[RealDigits[N[E], 10000], 2]]]];
Take[Map[#[[1]]&, StringPosition[s, "00"]], z] (*A293792*)
Take[Map[#[[1]]&, StringPosition[s, "01"]], z] (*A293793*)
Take[Map[#[[1]]&, StringPosition[s, "10"]], z] (*A293794*)
Take[Map[#[[1]]&, StringPosition[s, "11"]], z] (*A293795*)
(* Peter J. C. Moses, Oct 15 2017 *)
SequencePosition[RealDigits[E, 2, 250][[1]], {1, 0}][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 29 2019 *)

Crossrefs

Cf. A004593, A293792, A293793, A293795.

Sequence in context: A145604 A053569 A310123 * A115283 A078382 A075651

Adjacent sequences: A293791 A293792 A293793 * A293795 A293796 A293797

Keyword

nonn,easy,base

Author

Clark Kimberling, Oct 20 2017

Status

approved