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    Ulam Sequence

    Sequence description

    a_1 = 1; a_2 = 2; subsequent terms are the lowest numbers which are unique sums of two distinct earlier terms

    Sequence terms

    1, 2, 3, 4, 6, 8, 11, 13, 16, 18, 26, 28, 36, 38, 47, 48, 53, 57, 62, 69, 72, 77, 82, ...

    Table program

    Function[n, With[{Ulam = Compile[{{nmax, _Integer}, {init, _Integer, 1}, {s, _Integer}}, Module[{ulamhash = Table[0, {nmax}], ulam = init}, ulamhash[[ulam]] = 1; Do[If[Quotient[Plus @@ ulamhash[[i - ulam]], 2] == s, AppendTo[ulam, i]; ulamhash[[i]] = 1], {i, Last[init] + 1, nmax}]; ulam]]}, Ulam[14 n, {1, 2}, 1]]]

    Plot

    Plot

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