A080353 a(1)=5; for n>1, a(n)=a(n-1)+1 if n is already in the sequence, a(n)=a(n-1)+2 otherwise.

5, 7, 9, 11, 12, 14, 15, 17, 18, 20, 21, 22, 24, 25, 26, 28, 29, 30, 32, 33, 34, 35, 37, 38, 39, 40, 42, 43, 44, 45, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 79, 80, 81, 82, 83, 84, 86, 87, 88, 89

Offset

1,1

Comments

Conjecture: This sequence is equivalent to N \ A008478. - Michael De Vlieger, Jul 02 2025

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Benoit Cloitre, A study of a family of self-referential sequences, arXiv:2506.18103 [math.GM], 2025. See p. 13.

Benoit Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.

Benoit Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, arXiv:math/0305308 [math.NT], 2003.

Formula

a(n) = n + floor(sqrt(6*n)) + O(1).

Mathematica

a[1] = 5; a[n_] := a[n] = If[MemberQ[Array[a, n-1], n], a[n-1]+1, a[n-1]+2]; Array[a, 67] (* Jean-François Alcover, Oct 08 2018 *)

Crossrefs

Cf. A080036, A080037. Differences give A080354.

Sequence in context: A385595 A165513 A002342 * A184108 A254760 A279289

Adjacent sequences: A080350 A080351 A080352 * A080354 A080355 A080356

Keyword

nonn

Author

N. J. A. Sloane, Mar 20 2003

Status

approved