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

%I A355457 #7 Jul 03 2022 09:14:58
%S A355457 2,3,4,7,15,26,31,43,98,117,140,215,540,1945,22279,38459,39461,66869,
%T A355457 69328,4047994,4615259,5617480,5898979,9685120,9751023
%N A355457 Numbers k > 1 such that A354833(k) = k * A354833(k-1).
%C A355457 This sequence gives indexes of multiplicative steps in A354833.
%e A355457 For k = 7:
%e A355457 - A354833(7) = 91 = 7 * 13 = 7 * A354833(6),
%e A355457 - so 7 is a term.
%o A355457 (PARI) { 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)) }
%o A355457 (Python)
%o A355457 from itertools import count, islice
%o A355457 def agen():
%o A355457     an, seen = 1, {1}
%o A355457     for n in count(2):
%o A355457         t = an - n
%o A355457         if t not in seen and t >= 0: an = t
%o A355457         else: an *= n; yield n
%o A355457         seen.add(an)
%o A355457 print(list(islice(agen(), 25))) # _Michael S. Branicky_, Jul 02 2022
%Y A355457 Cf. A354833.
%K A355457 nonn,more
%O A355457 1,1
%A A355457 _Rémy Sigrist_, Jul 02 2022
%E A355457 a(20)-a(25) from _Michael S. Branicky_, Jul 02 2022