A080903 a(1)=1; for n>1, a(n)=a(n-1)+4 if n is already in the sequence, a(n)=a(n-1)+2 otherwise.

1, 3, 7, 9, 11, 13, 17, 19, 23, 25, 29, 31, 35, 37, 39, 41, 45, 47, 51, 53, 55, 57, 61, 63, 67, 69, 71, 73, 77, 79, 83, 85, 87, 89, 93, 95, 99, 101, 105, 107, 111, 113, 115, 117, 121, 123, 127, 129, 131, 133, 137, 139, 143, 145, 149, 151, 155, 157, 159

Offset

1,2

Comments

In the Fokkink-Joshi paper, this sequence is the Cloitre (0,1,4,2)-hiccup sequence. - Michael De Vlieger, Jul 29 2025

Links

Ivan Neretin, Table of n, a(n) for n = 1..1000

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.

Robbert Fokkink and Gandhar Joshi, On Cloitre's hiccup sequences, Ramanujan J. 69 (2026), 40. See pp. 2, 4 (Table 1), 14-15 (Lemma 15). See also arXiv:2507.16956 [math.CO], 2025. See pp. 2-3.

Mathematica

Fold[Append[#1, #1[[-1]] + If[MemberQ[#1, #2], 4, 2]] &, {1}, Range[2, 59]] (* Ivan Neretin, Mar 03 2016 *)

Crossrefs

Cf. A080578, A080900, A086398, A284753.

Sequence in context: A045572 A069254 A105585 * A172253 A104381 A136333

Adjacent sequences: A080900 A080901 A080902 * A080904 A080905 A080906

Keyword

nonn

Author

Benoit Cloitre, Apr 01 2003

Status

approved