A270344 Least squarefree number that has runs of exactly n nonsquarefree numbers directly preceding and succeeding it.

2, 17, 26, 2526, 5876126, 8061827, 8996188226, 5295909711327

Offset: 0

Author

Hartmut F. W. Hoft, Mar 15 2016

Keywords

• nonn
• more

Comments

The sequence appears to be monotone increasing, but the Mathematica implementation does not assume that.

Only a(0) and a(7) differ from A268330 in the numbers computed so far.

Crossrefs

Cf. A268330.

Programs

Mathematica

(* computes a(n), 1 <= n <= 5 *)
sfRun[n_]:=Module[{i=n}, While[SquareFreeQ[i], i++]; i-n]
nsfRun[n_]:=Module[{i=n}, While[!SquareFreeQ[i], i++]; i-n]
a270344[{low_, high_}]:=Module[{i, next, r, s, list=Table[{},5]}, For[i=low, i<=high, i+=next, r=nsfRun[i]; If[r==0, next=sfRun[i], s=nsfRun[i+r+1]; If[r==s, If[list[[r]]=={}, list[[r]]={i, i+r, i+2r}]; next=2r+2, next=r+1]]]; list]
Map[#[[2]]&, a270344[{0,10000000}]] (* data *)

Extensions

a(7) from Giovanni Resta, Apr 11 2016