A285764 A relative of the Hofstadter-Conway sequence A004001.

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

Offset

1,2

Comments

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

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 the Hofstadter-Conway sequence A004001 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

A285764:=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 3: elif n = 7 then 4: elif n = 8 then 5: elif n = 9 then 6: else A285764(A285764(n-3)) + A285764(n-A285764(n-3)): fi: end:

Crossrefs

Cf. A004001, A285763.

Sequence in context: A255070 A176001 A194272 * A025776 A120505 A029109

Adjacent sequences: A285761 A285762 A285763 * A285765 A285766 A285767

Keyword

nonn

Author

Nathan Fox, Apr 25 2017

Status

approved