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.

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

Amiram Eldar, Table of n, a(n) for n = 1..162

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

Cf. A071626, A357385, A357387.

Sequence in context: A065670 A105327 A260334 * A257939 A203607 A188977

Adjacent sequences: A357383 A357384 A357385 * A357387 A357388 A357389

Keyword

nonn

Author

Amiram Eldar, Sep 26 2022

Status

approved