A283628 Numbers n such that 4n - 3, 4n - 2, 4n - 1, 4n + 1, 4n + 2 and 4n + 3 are all squarefree.

1, 8, 9, 10, 17, 26, 27, 28, 35, 45, 46, 53, 54, 55, 64, 71, 80, 89, 98, 99, 100, 108, 109, 116, 117, 125, 136, 153, 154, 161, 170, 179, 189, 190, 197, 198, 199, 215, 224, 225, 226, 234, 235, 242, 251, 252, 260, 261, 278, 279, 280, 289, 297, 298, 305, 314, 315, 316, 323, 324, 325, 334, 341, 350

Offset

1,2

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

a(n) ~ kn with k around 5.42. - Charles R Greathouse IV, Mar 13 2017

a(n) ~ kn where k = Product_{p prime > 2} p^2/(p^2-6). - Michael R Peake, Mar 17 2017

Example

1 is in this sequence because 4*1 - 3 = 1, 4*1 - 2 = 2, 4*1 - 1 = 3, 4*1 + 1 = 5, 4*1 + 2 = 6 and 4*1 + 3 = 7 are all squarefree.

Mathematica

Select[Range@ 350, Function[n, Times @@ Boole@ Map[SquareFreeQ, 4 n + Flatten@ {-#, #} &@ Range@ 3] == 1]] (* Michael De Vlieger, Mar 17 2017 *)
Select[Range[400], AllTrue[4#+{1, 2, 3, -1, -2, -3}, SquareFreeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Nov 30 2019 *)

Prog

(Magma) [n: n in [1..300] | IsSquarefree(4*n-3) and IsSquarefree(4*n-2) and IsSquarefree(4*n-1) and IsSquarefree(4*n+1) and IsSquarefree(4*n+2) and IsSquarefree(4*n+3) ];
(PARI) is(n)=forstep(k=4*n-3, 4*n+3, [1, 1, 2, 1, 1], if(!issquarefree(k), return(0))); 1 \\ Charles R Greathouse IV, Mar 13 2017

Crossrefs

Cf. A005117.

Sequence in context: A054966 A130881 A235399 * A343860 A308809 A272142

Adjacent sequences: A283625 A283626 A283627 * A283629 A283630 A283631

Keyword

nonn

Author

Juri-Stepan Gerasimov, Mar 13 2017

Status

approved