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A354833 a(1)=1; for n > 1, a(n) = a(n-1) - n unless that result is already in the sequence or would be negative; otherwise, a(n) = a(n-1) * n.

%I A354833 #36 Jul 02 2023 22:31:54
%S A354833 1,2,6,24,19,13,91,83,74,64,53,41,28,14,210,194,177,159,140,120,99,77,
%T A354833 54,30,5,130,103,75,46,16,496,464,431,397,362,326,289,251,212,172,131,
%U A354833 89,3827,3783,3738,3692,3645,3597,3548,3498,3447,3395,3342,3288,3233,3177
%N A354833 a(1)=1; for n > 1, a(n) = a(n-1) - n unless that result is already in the sequence or would be negative; otherwise, a(n) = a(n-1) * n.
%H A354833 Rémy Sigrist, <a href="/A354833/b354833.txt">Table of n, a(n) for n = 1..22279</a>
%e A354833 a(7) = 91 because from the previous term (13) you cannot subtract 7, because you would get 6, which is already in the sequence, so multiply 13 by 7 to get 91.
%t A354833 a[1] = 1; a[n_] := a[n] = Module[{s = Array[a, n - 1], d}, If[(d = a[n - 1] - n) < 0 || MemberQ[s, d], n * a[n - 1], d]]; Array[a, 50] (* _Amiram Eldar_, Jun 07 2022 *)
%o A354833 (PARI) { seen = Map(); v = 1; for (n=1, 56, mapput(seen, v, 0); print1 (v", "); v=if (mapisdefined(seen, w=v-(n+1)) || w<0, v*(n+1), w)) } \\ _Rémy Sigrist_, Jul 02 2022
%o A354833 (Python)
%o A354833 from itertools import count, islice
%o A354833 def agen():
%o A354833     an, seen = 1, {1}
%o A354833     yield 1
%o A354833     for n in count(2):
%o A354833         t = an - n
%o A354833         an = t if t not in seen and t >= 0 else an*n
%o A354833         yield an
%o A354833         seen.add(an)
%o A354833 print(list(islice(agen(), 56))) # _Michael S. Branicky_, Jul 02 2022
%Y A354833 Cf. A005132, A200044.
%Y A354833 Cf. A355457 (Multiplicative steps).
%K A354833 nonn
%O A354833 1,2
%A A354833 _Kelvin Voskuijl_, Jun 07 2022