A285761 A slow relative of Hofstadter's Q sequence.

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

Offset: 1

Author

Nathan Fox, Apr 25 2017

Keywords

• nonn

Comments

a(n) is the solution to the recurrence relation a(n) = a(n-4-a(n-1)) + a(n-4-a(n-4)), with the initial conditions: a(1) = 1, a(2) = 2, a(3) = a(4) = a(5) = 3, a(6) = a(7) = a(8) = 4, a(9) = a(10) = 5.

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, A285759, A285760, A285762.

Programs

Maple

A285761:=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 3: elif n = 5 then 3: elif n = 6 then 4: elif n = 7 then 4: elif n = 8 then 4: elif n = 9 then 5: elif n = 10 then 5: else A285761(n-4-A285761(n-1)) + A285761(n-4-A285761(n-4)): fi: end: