A283883 Relative of Hofstadter Q-sequence: a(n) = max(0, n+117) for n <= 0; a(n) = a(n-a(n-1)) + a(n-a(n-2)) for n > 0.

3, 118, 119, 5, 120, 6, 7, 121, 123, 10, 8, 123, 127, 12, 124, 14, 129, 11, 128, 132, 16, 13, 17, 15, 131, 20, 20, 242, 123, 24, 32, 238, 3, 32, 357, 5, 238, 3, 5, 595, 5, 238, 3, 5, 833, 5, 238, 3, 5, 1071, 5, 238, 3, 5, 1309, 5, 238, 3, 5, 1547, 5, 238, 3, 5, 1785, 5, 238, 3, 5, 2023, 5, 238, 3, 5, 2261

Offset: 1

Author

Nathan Fox, Mar 19 2017

Keywords

• nonn
• fini

Comments

Sequences like this are more naturally considered with the first nonzero term in position 1. But this sequence would then match A000027 for its first 117 terms.

This sequence has exactly 3346939303954 terms (of positive index). a(3346939303954) = 0, so an attempt to calculate a(3346939303955) would refer to itself.

Links

• Nathan Fox, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005185, A274058, A283883.

Programs

Maple

A283883:=proc(n) option remember: if n <= 0 then max(0, n+117): else A283883(n-A283883(n-1)) + A283883(n-A283883(n-2)): fi: end:

Formula

If the index is between 35 and 122 (inclusive), then a(5n) = 238n-1309, a(5n+1) = 5, a(5n+2) = 238, a(5n+3) = 3, a(5n+4) = 5.

If the index is between 128 and 4525 (inclusive), then a(5n) = 4641, a(5n+1) = 3, a(5n+2) = 5, a(5n+3) = 4641n-106981, a(5n+4) = 5.

If the index is between 4531 and 4093008 (inclusive), then a(5n) = 5, a(5n+1) = 4093124n-3700188737, a(5n+2) = 5, a(5n+3) = 4093124, a(5n+4) = 3.

If the index is between 4093008 and 3346939303796 (inclusive), then a(5n) = 5, a(5n+1) = 3346939303911, a(5n+2) = 3, a(5n+3) = 5, a(5n+4) = 3346939303911n-2739804514185637724.