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
Keywords
Examples
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.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Crossrefs
Cf. A005117.
Programs
-
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) ];
-
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 *) -
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
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