A357387 Starts of record-length runs of consecutive positive integers with the same value of A071626.

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, ...

Links

Table of n, a(n) for n=1..23.

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

Cf. A071626, A357385, A357386.

Sequence in context: A050895 A184426 A293408 * A369237 A097022 A370114

Adjacent sequences: A357384 A357385 A357386 * A357388 A357389 A357390

Keyword

nonn,more

Author

Amiram Eldar, Sep 26 2022

Status

approved