A373234 Relative of Hofstadter Q-sequence: a(n) = max(0, n+196) for n <= 0; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 0.

6, 197, 198, 199, 9, 200, 201, 202, 12, 203, 204, 205, 15, 206, 207, 17, 209, 18, 209, 211, 212, 22, 21, 403, 397, 9, 18, 412, 415, 205, 22, 226, 231, 209, 27, 36, 233, 402, 200, 39, 234, 240, 204, 42, 236, 243, 16, 235, 243, 223, 40, 235, 55, 416, 212, 46, 245, 256, 25, 38, 58, 835, 406, 200, 61, 71, 455, 394, 194, 72, 268, 270, 7, 457, 395

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 196 terms.

This sequence has exactly 223 terms (of positive index). a(223) = 0, so an attempt to calculate a(224) would refer to itself.

Without the convention that a(n) = 0 for n <= -196, this sequence would have exactly 24 terms (of positive index), since computing a(25) refers to a(-378).

If 196 in this sequence's definition is replaced by any larger number congruent to 0 mod 7, the behavior is essentially the same, though the quasilinear part (see Formula section) lasts longer.

Links

Nathan Fox, Table of n, a(n) for n = 1..223

Formula

If the index is between 67 and 195 (inclusive), then a(7n) = 7n+2, a(7n+1) = 7n+198, a(7n+2) = 7n+200, a(7n+3) = 7, a(7n+4) = 2n+437, a(7n+5) = n+385, a(7n+6) = 194.

Crossrefs

Cf. A005185, A267501, A278055, A373235, A373236, A373237, A373238, A274058, A373239.

Sequence in context: A200824 A351888 A340557 * A305167 A112845 A373238

Adjacent sequences: A373231 A373232 A373233 * A373235 A373236 A373237

Keyword

nonn,fini,full

Author

Nathan Fox, May 28 2024

Status

approved