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

1,2

Links

Table of n, a(n) for n=1..63.

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

Example

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.

Mathematica

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

Prog

(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) ];
(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

Crossrefs

Cf. A005117, A283628.

Sequence in context: A354695 A293066 A104253 * A191581 A192896 A115030

Adjacent sequences: A283665 A283666 A283667 * A283669 A283670 A283671

Keyword

nonn

Author

Juri-Stepan Gerasimov, Mar 13 2017

Status

approved