Decimal notation to se-notation

    %%%%%%%%%% Most numbers up to 20 characters
%%%%%%%%%%%%%%%%%%%% Mathematica code to generate the strings

    gen[n_] :=
     Select[
      StringJoin /@ (# /. {1 -> "s", -1 -> "e"} & /@
         (Prepend[#,
             1] & /@ (Append[#, -1] & /@ (
              Select[
               Permutations[
                Join[ConstantArray[1, n - 1], ConstantArray[-1, n - 1]]],
               FreeQ[Table[Plus @@ Take[#, k] >= 0, {k, 1, Length@#}],
                 False] &
               ]
              )))),
      StringFreeQ[#, "esee"] &]


    SortBy[
      Flatten[
       Table[{If[# > 10^100, ">10^100", #] &@eval[#], #} & /@ gen[n], {n,
         1, 10}],
       1],
      First] // TableForm

    %%%%%%%%%%%%%%%%%%%% Mathematica code to translate the strings to decimal

    R = 10^50;

    primePower[exps_] :=
     Times @@ Thread@Power[Prime@Range@Length@exps, exps]

    stringPrimePower[string_] :=
     If[# < R || # == "abort", ToString@#, "abort"] &@(primePower@
        Cases[ToExpression[
          StringCases[string, DigitCharacter ..]], _Integer])

    powersToNumber[string_] :=
     If[StringFreeQ[string, "abort"],
      StringReplace[
       StringReplace[
        string,
        RegularExpression["s" <> "([^se]+)" <> "e"] -> "(" <> "$1" <> ")"],
       "(" ~~ x__ ~~ ")" :> "S" <> stringPrimePower[x] <> "E"],
      "abort"]

    eval[string_] :=
     ToExpression@StringDrop[StringDrop[
        FixedPoint[powersToNumber,
         StringReplace[StringReplace[string, "se" -> "S0E"],
          "sS0Ee" -> "S1E"]],
        1], -1]