A354833 -id:A354833 - cp's OEIS frontend

A355457 Numbers k > 1 such that A354833(k) = k * A354833(k-1).

2, 3, 4, 7, 15, 26, 31, 43, 98, 117, 140, 215, 540, 1945, 22279, 38459, 39461, 66869, 69328, 4047994, 4615259, 5617480, 5898979, 9685120, 9751023

Offset: 1

Rémy Sigrist, Jul 02 2022

This sequence gives indexes of multiplicative steps in A354833.

			For k = 7:
- A354833(7) = 91 = 7 * 13 = 7 * A354833(6),
- so 7 is a term.

Cf. A354833.

{ seen = Map(); v = 1; for (n=2, oo, mapput(seen, v, 0); v=if (mapisdefined(seen, w=v-n) || w<0, print1 (n", "); v*n, w)) }

from itertools import count, islice
def agen():
    an, seen = 1, {1}
    for n in count(2):
        t = an - n
        if t not in seen and t >= 0: an = t
        else: an *= n; yield n
        seen.add(an)
print(list(islice(agen(), 25))) # Michael S. Branicky, Jul 02 2022

a(20)-a(25) from Michael S. Branicky, Jul 02 2022

A363962 a(1)=1; for n > 1, if n appears in the sequence then a(n) = lastindex(n), where lastindex(n) is the index of the last appearance of n. Otherwise 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.

Original entry on oeis.org

1, 2, 6, 24, 19, 3, 21, 13, 4, 40, 29, 17, 8, 112, 97, 81, 12, 216, 5, 100, 7, 154, 131, 4, 100, 74, 47, 1316, 11, 330, 299, 267, 234, 200, 165, 129, 92, 54, 15, 10, 410, 368, 325, 281, 236, 190, 27, 1296, 1247, 1197, 1146, 1094, 1041, 38, 2090, 2034, 1977, 1919, 1860, 1800, 1739, 1677, 1614

Offset: 1

Kelvin Voskuijl, Jun 29 2023

nonn

			a(6) = 3, as a(3) = 6 = n, thus a(6) = 3.
a(28) = 1316 because subtracting 28 from the previous term (47) would give 19, which is already in the sequence, so multiply 47 by 28 to get 1316.
a(100) = 25, as a(25) = 100 = n, thus a(100) = 25.

Cf. A005132, A340612, A354833, A362332.

function a = A363962( max_n )
    a = 1;
    for n = 2:max_n
        r = find(a == n,1,'last');
        if ~isempty(r)
            a(n) = r;
        else
            k = a(n-1) - n;
            if k > 0 && isempty(find(a == k, 1))
                a(n) = k;
            else
                a(n) = a(n-1) * n;
            end
        end
    end
end % Thomas Scheuerle, Jul 03 2023

a[1] = 1; a[n_] := a[n] = Module[{s = Array[a, n - 1], a1}, If[MemberQ[s, n], Position[s, n][[-1, 1]], a1 = a[n - 1] - n; If[a1 < 0 || MemberQ[s, a1], a[n - 1]*n, a1]]]; Array[a, 100] (* Amiram Eldar, Jul 23 2023 *)

cp's OEIS Frontend

A355457 Numbers k > 1 such that A354833(k) = k * A354833(k-1).

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