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.

1, 2, 6, 24, 19, 13, 91, 83, 74, 64, 53, 41, 28, 14, 210, 194, 177, 159, 140, 120, 99, 77, 54, 30, 5, 130, 103, 75, 46, 16, 496, 464, 431, 397, 362, 326, 289, 251, 212, 172, 131, 89, 3827, 3783, 3738, 3692, 3645, 3597, 3548, 3498, 3447, 3395, 3342, 3288, 3233, 3177

Offset

1,2

Links

Rémy Sigrist, Table of n, a(n) for n = 1..22279

Example

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.

Mathematica

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 *)

Prog

(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
(Python)
from itertools import count, islice
def agen():
    an, seen = 1, {1}
    yield 1
    for n in count(2):
        t = an - n
        an = t if t not in seen and t >= 0 else an*n
        yield an
        seen.add(an)
print(list(islice(agen(), 56))) # Michael S. Branicky, Jul 02 2022

Crossrefs

Cf. A005132, A200044.

Cf. A355457 (Multiplicative steps).

Sequence in context: A263692 A363962 A319544 * A124900 A068819 A060068

Adjacent sequences: A354830 A354831 A354832 * A354834 A354835 A354836

Keyword

nonn

Author

Kelvin Voskuijl, Jun 07 2022

Status

approved