A285757 a(n) = a(n - a(n - 2)) + a(n - a(n - 8)), with a(i) = i for 1 <= i <= 9.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 11, 12, 12, 12, 13, 14, 15, 16, 16, 16, 17, 18, 18, 18, 19, 20, 21, 22, 22, 22, 22, 22, 23, 24, 24, 24, 25, 26, 27, 28, 28, 28, 29, 30, 30, 30, 31, 32, 33, 34, 34, 34, 34, 34, 35, 36, 36, 36, 37, 38, 39

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.

This sequence can be obtained from A063882 using a construction of Isgur et al.

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, A285758, A285759, A285760, A285761, A285762.

Programs

Maple

A285757:=proc(n) option remember: if n <= 0 then 0: elif n = 1 then 1: elif n = 2 then 2: elif n = 3 then 3: elif n = 4 then 4: elif n = 5 then 5: elif n = 6 then 6: elif n = 7 then 7: elif n = 8 then 8: elif n = 9 then 9: else A285757(n-A285757(n-2)) + A285757(n-A285757(n-8)): fi: end: