A362332 -id:A362332 - cp's OEIS frontend

A362698 For n > 1, if n appears in the sequence, a(n) = a(n-1) - n if nonnegative and not already in the sequence, otherwise a(n) = a(n-1) + n. Otherwise a(n+1) = a(n)/(n+1) if (n+1)|a(n), otherwise a(n)(n+1), a(1) = 1 and a(2) = 12.

1, 2, 6, 24, 120, 114, 798, 6384, 57456, 574560, 6320160, 526680, 6846840, 489060, 32604, 521664, 8868288, 159629184, 8401536, 168030720, 3528645120, 160392960, 3689038080, 3689038056, 92225951400, 2397874736400, 64742617882800, 1812793300718400, 52571005720833600

Offset: 1

Kelvin Voskuijl, Jul 07 2023

nonn

			a(2) = 2, as a(1) = 1 and 1 times 2 is 2.
a(6) = 114, as a(3) = 6 = n, thus a(6) = a(5) - 6 =  114.
a(7) = 798, as a(6) = 114 and 7 times 114 is 798.

Michael De Vlieger, Table of n, a(n) for n = 1..1996
Michael De Vlieger, Log log scatterplot of log_10 a(n), n = 2..2^18.

Cf. A008336, A362332, A340612.

nn = 120; c[] := False; Array[Set[{a[#], c[#]}, {#, True}] &, 2]; j = 2; Do[k = If[c[n], If[And[! c[#], # >= 0], #, j + n] &[j - n], If[Divisible[j, n], j/n, j n]]; Set[{a[n], c[k], j}, {k, True, k}], {n, 3, nn}]; Array[a, nn] (* _Michael De Vlieger, Aug 30 2023 *)

More terms from Michael De Vlieger, Aug 30 2023

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

A362698 For n > 1, if n appears in the sequence, a(n) = a(n-1) - n if nonnegative and not already in the sequence, otherwise a(n) = a(n-1) + n. Otherwise a(n+1) = a(n)/(n+1) if (n+1)|a(n), otherwise a(n)(n+1), a(1) = 1 and a(2) = 12.

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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.

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cp's OEIS Frontend

A362698 For n > 1, if n appears in the sequence, a(n) = a(n-1) - n if nonnegative and not already in the sequence, otherwise a(n) = a(n-1) + n. Otherwise a(n+1) = a(n)/(n+1) if (n+1)|a(n), otherwise a(n)*(n+1), a(1) = 1 and a(2) = 1*2.

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Extensions

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.

Views

Author

Keywords

Examples

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Programs

MATLAB

Mathematica

A362698 For n > 1, if n appears in the sequence, a(n) = a(n-1) - n if nonnegative and not already in the sequence, otherwise a(n) = a(n-1) + n. Otherwise a(n+1) = a(n)/(n+1) if (n+1)|a(n), otherwise a(n)(n+1), a(1) = 1 and a(2) = 12.