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

1,1

Links

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

Formula

A073484(a(n)) = 3.

Example

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.

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 *)

Crossrefs

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

Sequence in context: A306864 A306877 A073495 * A353552 A232040 A054817

Adjacent sequences: A073486 A073487 A073488 * A073490 A073491 A073492

Keyword

nonn

Author

Reinhard Zumkeller, Aug 03 2002

Status

approved