A283882 Relative of Hofstadter Q-sequence: a(n) = max(0, n+67) for n <= 0; a(n) = a(n-a(n-1)) + a(n-a(n-2)) for n > 0.

3, 68, 69, 5, 70, 6, 7, 71, 73, 10, 8, 73, 77, 12, 74, 14, 79, 11, 78, 82, 16, 13, 17, 15, 81, 20, 20, 142, 73, 24, 32, 138, 3, 32, 207, 5, 138, 3, 5, 345, 5, 138, 3, 5, 483, 5, 138, 3, 5, 621, 5, 138, 3, 5, 759, 5, 138, 3, 5, 897, 5, 138, 3, 5, 1035, 5, 138, 3, 5, 1173, 5, 138, 5, 8, 1311

Offset

1,1

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 67 terms.

Links

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

Formula

If the index is between 35 and 72 (inclusive), then a(5n) = 138n-759, a(5n+1) = 5, a(5n+2) = 138, a(5n+3) = 3, a(5n+4) = 5.

If the index is between 78 and 1245 (inclusive), then a(5n) = 1311, a(5n+1) = 3, a(5n+2) = 5, a(5n+3) = 1311n-17181, a(5n+4) = 5.

If the index is between 1251 and 309192 (inclusive), then a(5n) = 5, a(5n+1) = 19047817435n-1178393232110703, a(5n+2) = 5, a(5n+3) = 19047817435, a(5n+4) = 3.

If the index is between 309336 and 19047817368 (inclusive), then a(5n) = 5, a(5n+1) = 309258n-76697295, a(5n+2) = 5, a(5n+3) = 309258, a(5n+4) = 3.

If the index is at least 19047817371, then a(5n) = 5*A272611(n-3809563474), a(5n+1) = 5*A272611(n-3809563473), a(5n+2) = 5*A272612(n-3809563473), a(5n+3) = 19047817435*A272613(n-3809563473), a(5n+4) = 4. This pattern lasts as long as A272611 exists (which is conjectured to be forever).

Maple

A283882:=proc(n) option remember: if n <= 0 then max(0, n+67): else A283882(n-A283882(n-1)) + A283882(n-A283882(n-2)): fi: end:

Crossrefs

Cf. A005185, A272610, A272611, A272612, A272613, A274058, A283883.

Sequence in context: A182367 A091872 A079320 * A073163 A324082 A279491

Adjacent sequences: A283879 A283880 A283881 * A283883 A283884 A283885

Keyword

nonn

Author

Nathan Fox, Mar 19 2017

Status

approved