A283668 Numbers n such that 36n - 7, 36n - 6, 36n - 5, 36n - 3, 36n - 2, 36n - 1, 36n + 1, 36n + 2, 36n + 3, 36n + 5, 36n + 6 and 36n + 7 are all squarefree.

1, 3, 6, 11, 22, 25, 31, 35, 36, 39, 49, 51, 58, 65, 67, 69, 81, 85, 86, 92, 97, 99, 100, 110, 115, 119, 125, 126, 133, 135, 142, 144, 149, 150, 153, 161, 164, 165, 167, 169, 172, 174, 175, 176, 186, 194, 199, 201, 206, 208, 210, 214, 217, 224, 231, 235, 236, 239, 240, 242, 244, 247, 251

Offset: 1

Author

Juri-Stepan Gerasimov, Mar 13 2017

Keywords

• nonn

Examples

			1 is in this sequence because 36*1 - 7 = 29, 36*1 - 6 = 30, 36*1 - 5 = 31, 36*1 - 3 = 33, 36*1 - 2 = 34, 36*1 - 1 = 35, 36*1 + 1 = 37, 36*1 + 2 = 38, 36*1 + 3 = 39, 36*1 + 5 = 41, 36*1 + 6 = 42 and 36*1 + 7 = 43 are all squarefree.
		

Crossrefs

Cf. A005117, A283628.

Programs

Magma

[n: n in [1..300] | IsSquarefree(36*n-7) and IsSquarefree(36*n-6) and IsSquarefree(36*n-5) and IsSquarefree(36*n-3) and IsSquarefree(36*n-2) and IsSquarefree(36*n-1) and IsSquarefree(36*n+1) and IsSquarefree(36*n+2) and IsSquarefree(36*n+3) and IsSquarefree(36*n+5) and IsSquarefree(36*n+6) and IsSquarefree(36*n+7) ];

Mathematica

Select[Range@ 256, Function[n, Times @@ Boole@ Map[SquareFreeQ, 36 n + Flatten@ {-#, #} &@ Drop[Range@ 7, {4}]] == 1]] (* Michael De Vlieger, Mar 13 2017 *)

PARI

isok(n) = forstep(k=36*n - 7, 36*n + 7, [1,1,2,1,1,2,1,1,2,1,1], if(!issquarefree(k), return (0))); 1;
for(n=1, 251, if(isok(n), print1(n,", "))) \\ Indranil Ghosh, Mar 13 2017

Formula

a(n) = A283628(9n) = A283628(9n-1) + 1 = A283628(9n+1) - 1.

a(n) ~ k*n where k = Product_{ p prime > 3} p^2/(p^2 - 12) = 3.7192316.... - Michael R Peake, Mar 16 2017