A073489 Squarefree numbers having exactly three prime gaps.

1870, 2090, 2470, 2530, 2990, 3190, 3410, 3458, 3770, 3910, 4030, 4070, 4186, 4510, 4730, 4810, 4930, 5170, 5187, 5270, 5278, 5330, 5474, 5510, 5590, 5642, 5830, 5890, 6110, 6279, 6290, 6490, 6710, 6734, 6890, 6902, 6970, 7030, 7130, 7310, 7370, 7378

Offset: 1

Author

Reinhard Zumkeller, Aug 03 2002

Keywords

• nonn

Examples

			1870 is a term, as 1870 = 2*5*11*17 = with three gaps: between 2 and 5, between 5 and 11 and between 11 and 17.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005117, A073484, A073486, A073488, A073495.

Programs

Mathematica

q[n_] := SequenceCount[FactorInteger[n][[;; , 1]], {p1_, p2_} /; p2 != NextPrime[p1], Overlaps -> True] == 3; Select[Range[7500], SquareFreeQ[#] && q[#] &] (* Amiram Eldar, Apr 10 2021 *)
sfQ[n_]:=SquareFreeQ[n]&&Total[Boole[NextPrime[#[[1]]]!=#[[2]]&/@ Partition[ FactorInteger[n][[All,1]],2,1]]]==3; Select[Range[7500],sfQ] (* Harvey P. Dale, Aug 29 2021 *)

Formula

A073484(a(n)) = 3.