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A357386
a(n) is the start of the least run of exactly n consecutive positive integers with the same value of A071626, or -1 if no such run exists.
2
1, 2, 116, 6, 10, 290, 15, 333, 136, 55, 22, 102, 410, 119, 477, 232, 68, 261, 451, 2343, 153, 348, 708, 492, 1037, 377, 976, 826, 174, 615, 1940, 656, 1422, 8642, 1711, 7712, 10382, 3232, 5921, 9089, 3434, 2286, 2556, 1988, 5617, 6040, 6576, 17025, 12939, 6194, 19694
OFFSET
1,2
COMMENTS
The common values of A071626 in each run are 0, 1, 12, 3, 4, 18, 5, 20, 13, 9, 6, 12, 22, 13, 23, 17, 10, 18, 23, ...
LINKS
EXAMPLE
a(2) = 2 since A071626(2) = A071626(3) = 1, A071626(1) = 0 and A071626(4) = 2.
a(3) = 116 since A071626(116) = A071626(117) = A071626(118) = 12, A071626(115) = 11 and A071626(119) = 13, and 116 is the least integer with this property.
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}; Do[i = FirstPosition[d, k]; If[MissingQ[i], Break[]]; AppendTo[seq, ind[[i[[1]]]] + 1], {k, 2, Max[d]}]; seq
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Sep 26 2022
STATUS
approved