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A357387
Starts of record-length runs of consecutive positive integers with the same value of A071626.
1
1, 2, 6, 10, 15, 22, 68, 153, 174, 615, 656, 1422, 1711, 1846, 2425, 7164, 8791, 13988, 42755, 48290, 186108, 221131, 3860731
OFFSET
1,2
COMMENTS
The corresponding record lengths are 1, 2, 4, 5, 7, 11, 17, 21, 29, 30, 32, 33, 35, 52, 57, 64, 78, 86, 96, 113, 122, 208, 221, ...
The common values of A071626 in each run are 0, 1, 3, 4, 5, 6, 10, 14, 15, 26, 27, 38, 40, 42, 48, 77, 84, 103, 172, 182, 335, 365, 1338, ...
FORMULA
2 is a term since it starts a run of 2 consecutive integers with the same value of A071626: A071626(2) = A071626(3) = 1.
6 is the next term since it starts a run of 4 consecutive integers with the same value of A071626: A071626(6) = A071626(7) = A071626(8) = A071626(9) = 3.
MATHEMATICA
s[n_] := Length[Union[FactorInteger[n!][[;; , 2]]]]; s[1] = 0; ind = Position[Differences[Table[s[n], {n, 1, 1000}]], _?(# != 0 &)] // Flatten; d = Differences[ind]; seq = {1}; dm = -1; Do[If[d[[i]] > dm, dm = d[[i]]; AppendTo[seq, ind[[i]] + 1]], {i, 1, Length[d]}]; seq
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Sep 26 2022
STATUS
approved