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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.

%I A363962 #22 Aug 26 2023 02:52:43
%S A363962 1,2,6,24,19,3,21,13,4,40,29,17,8,112,97,81,12,216,5,100,7,154,131,4,
%T A363962 100,74,47,1316,11,330,299,267,234,200,165,129,92,54,15,10,410,368,
%U A363962 325,281,236,190,27,1296,1247,1197,1146,1094,1041,38,2090,2034,1977,1919,1860,1800,1739,1677,1614
%N 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.
%e A363962 a(6) = 3, as a(3) = 6 = n, thus a(6) = 3.
%e A363962 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.
%e A363962 a(100) = 25, as a(25) = 100 = n, thus a(100) = 25.
%t A363962 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 *)
%o A363962 (MATLAB)
%o A363962 function a = A363962( max_n )
%o A363962     a = 1;
%o A363962     for n = 2:max_n
%o A363962         r = find(a == n,1,'last');
%o A363962         if ~isempty(r)
%o A363962             a(n) = r;
%o A363962         else
%o A363962             k = a(n-1) - n;
%o A363962             if k > 0 && isempty(find(a == k, 1))
%o A363962                 a(n) = k;
%o A363962             else
%o A363962                 a(n) = a(n-1) * n;
%o A363962             end
%o A363962         end
%o A363962     end
%o A363962 end % _Thomas Scheuerle_, Jul 03 2023
%Y A363962 Cf. A005132, A340612, A354833, A362332.
%K A363962 nonn
%O A363962 1,2
%A A363962 _Kelvin Voskuijl_, Jun 29 2023