A285762 A slow relative of Hofstadter's Q sequence.

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

Offset

1,2

Comments

a(n) is the solution to the recurrence relation a(n) = a(n-12-a(n-3)) + a(n-12-a(n-12)), with a(1) through a(33) as initial conditions.

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 A285761 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

Maple

A285762:=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: elif n = 10 then 9: elif n = 11 then 9: elif n = 12 then 9: elif n = 13 then 9: elif n = 14 then 9: elif n = 15 then 9: elif n = 16 then 10: elif n = 17 then 11: elif n = 18 then 12: elif n = 19 then 12: elif n = 20 then 12: elif n = 21 then 12: elif n = 22 then 12: elif n = 23 then 12: elif n = 24 then 12: elif n = 25 then 13: elif n = 26 then 14: elif n = 27 then 15: elif n = 28 then 15: elif n = 29 then 15: elif n = 30 then 15: elif n = 31 then 15: elif n = 32 then 15: elif n = 33 then 15: else A285762(n-12-A285762(n-3)) + A285762(n-12-A285762(n-12)): fi: end:

Crossrefs

Cf. A005185, A063882, A285757, A285758, A285759, A285760, A285761.

Sequence in context: A257779 A328865 A329623 * A185137 A368906 A368993

Adjacent sequences: A285759 A285760 A285761 * A285763 A285764 A285765

Keyword

nonn

Author

Nathan Fox, Apr 25 2017

Status

approved