A373239 - OEIS

A373239

Relative of Hofstadter Q-sequence: a(n) = max(0, n+118) for n <= 0; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 0.

6, 119, 120, 121, 9, 122, 123, 124, 12, 125, 126, 127, 15, 128, 129, 17, 131, 18, 131, 133, 134, 22, 21, 247, 241, 9, 18, 256, 259, 127, 22, 148, 153, 131, 27, 36, 155, 246, 122, 39, 156, 162, 126, 42, 158, 165, 16, 157, 165, 145, 40, 157, 55, 260, 134, 46, 167, 178, 25, 38, 58, 523, 250, 122, 61, 71, 299, 238, 116, 72, 190, 192

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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 118 terms.

This sequence has exactly 127 terms (of positive index). a(127) = 0, so an attempt to calculate a(128) would refer to itself.

Without the convention that a(n) = 0 for n <= -118, this sequence would have exactly 24 terms (of positive index), since computing a(25) refers to a(-222).

If 118 in this sequence's definition is replaced by any larger number congruent to 6 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..127

FORMULA

If the index is between 67 and 118 (inclusive), then a(7n) = 7n+2, a(7n+1) = 7n+120, a(7n+2) = 7n+122, a(7n+3) = 7, a(7n+4) = 2n+281, a(7n+5) = n+229, a(7n+6) = 116.

CROSSREFS

Cf. A005185, A267501, A278055, A373234, A373235, A373236, A373237, A373238, A274058.

Sequence in context: A218713 A360426 A054957 * A271648 A353691 A290341

Adjacent sequences: A373236 A373237 A373238 * A373240 A373241 A373242

KEYWORD

nonn,fini,full

AUTHOR

Nathan Fox, May 28 2024

STATUS

approved