A285759 a(n) = a(n - 1 - a(n - 1)) + a(n - 1 - a(n - 4)), with a(1) = 1, a(2) = 1, a(3) = 1, a(4) = 2.

1, 1, 1, 2, 2, 3, 3, 4, 5, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 10, 10, 11, 11, 12, 13, 13, 14, 14, 15, 15, 16, 17, 17, 17, 18, 18, 19, 19, 20, 20, 20, 21, 21, 22, 23, 23, 24, 24, 25, 25, 26, 27, 27, 27, 28, 28, 29, 29, 30, 31, 31, 32, 32, 33

Offset: 1

Author

Nathan Fox, Apr 25 2017

Keywords

• nonn

Comments

The sequence a(n) is monotonic, with successive terms increasing by 0 or 1. So the sequence hits every positive integer.

Links

• Nathan Fox, Table of n, a(n) for n = 1..10000
• A. Isgur, R. Lech, S. Moore, S. Tanny, Y. Verberne, and Y. Zhang, Constructing New Families of Nested Recursions with Slow Solutions, SIAM J. Discrete Math., 30(2), 2016, 1128-1147. (20 pages); DOI:10.1137/15M1040505

Crossrefs

Cf. A005185, A063882, A285757, A285758, A285760, A285761, A285762.

Programs

Maple

A285759:=proc(n) option remember: if n <= 0 then 0: elif n = 1 then 1: elif n = 2 then 1: elif n = 3 then 1: elif n = 4 then 2: else A285759(n-1-A285759(n-1)) + A285759(n-1-A285759(n-4)): fi: end: