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A274058 Relative of Hofstadter Q-sequence: a(n) = max(0, n+32478) for n <= 0; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 0. 9
6, 32479, 32480, 32481, 9, 32482, 32483, 32484, 12, 32485, 32486, 32487, 15, 32488, 32489, 17, 32491, 18, 32491, 32493, 32494, 22, 21, 64967, 64961, 9, 18, 64976, 64979, 32487, 22, 32508, 32513, 32491, 27, 36, 32515, 64966, 32482, 39, 32516, 32522 (list; graph; refs; listen; history; text; internal format)
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 32478 terms.
This sequence has exactly 37025 terms (of positive index). a(37025) = 0, so an attempt to calculate a(37026) would refer to itself.
Without the convention that a(n) = 0 for n <= -32478, this sequence would have exactly 24 terms (of positive index), since computing a(25) refers to a(-64942).
If 32478 in this sequence's definition is replaced by any larger number congruent to 5 mod 7, the behavior is essentially the same, though the quasilinear part (see Formula section) lasts longer.
LINKS
N. Fox, Hofstadter-like Sequences over Nonstandard Integers", Talk given at the Rutgers Experimental Mathematics Seminar, November 10 2016.
FORMULA
If the index is between 67 and 32479 (inclusive), then a(7n) = 7n+2, a(7n+1) = 7n+32480, a(7n+2) = 7n+32482, a(7n+3) = 7, a(7n+4) = 2n+65001, a(7n+5) = n+64949, a(7n+6) = 32476.
MATHEMATICA
a[n_] := a[n] = If[n <= 0, Max[0, n + 2^15 - 290], a[n - a[n - 1]] + a[n - a[n - 2]] + a[n - a[n - 3]]]; Array[a, 42] (* Robert G. Wilson v, Mar 19 2017 *)
CROSSREFS
Sequence in context: A134728 A127488 A294322 * A182790 A306667 A172812
KEYWORD
nonn,fini,full
AUTHOR
Nathan Fox, Nov 10 2016
EXTENSIONS
Formula and definition corrected by Nathan Fox, Mar 18 2017
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)