A003157 A self-generating sequence (see Comments in A003156 for the definition). (Formerly M2713)

3, 8, 11, 14, 19, 24, 29, 32, 35, 40, 43, 46, 51, 54, 57, 62, 67, 72, 75, 78, 83, 88, 93, 96, 99, 104, 109, 114, 117, 120, 125, 128, 131, 136, 139, 142, 147, 152, 157, 160

Offset

1,1

Comments

Indices of c in the sequence closed under a -> abc, b -> a, c -> a, starting with a(1) = a; see A092606 where a = 0, b = 2, c = 1. - Philippe Deléham, Apr 12 2004

These are the positions of 1 in A286044; complement of A286045; conjecture: a(n)/n -> 4. - Clark Kimberling, May 07 2017

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

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

L. Carlitz, R. Scoville, and V. E. Hoggatt, Jr., Representations for a special sequence, Fibonacci Quarterly 10.5 (1972), 499-518, 550.

Formula

Numbers n such that A003159(n) is even. a(n) = A003158(n) + 1 = A036554(n) + n. - Philippe Deléham, Feb 22 2004

Example

As a word, A286044 = 001000010010010000100..., in which 1 is in positions a(n) for n>=1.  - Clark Kimberling, May 07 2017

Mathematica

s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {1, 0}}] &, {0}, 9] (* Thue-Morse, A010060 *)
w = StringJoin[Map[ToString, s]]
w1 = StringReplace[w, {"011" -> "0"}]
st = ToCharacterCode[w1] - 48 (* A286044 *)
Flatten[Position[st, 0]]  (* A286045 *)
Flatten[Position[st, 1]]  (* A003157 *)
(* Clark Kimberling, May 07 2017 *)

Crossrefs

Cf. A003156, A003158, A010060, A286044, A286045.

Sequence in context: A366582 A051245 A265897 * A310281 A287365 A257336

Adjacent sequences: A003154 A003155 A003156 * A003158 A003159 A003160

Keyword

nonn

Author

N. J. A. Sloane

Status

approved