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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A024495 A293066 A104253 * A191581 A192896 A115030

Adjacent sequences:  A283665 A283666 A283667 * A283669 A283670 A283671

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, Mar 13 2017

STATUS

approved

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Last modified July 27 17:09 EDT 2021. Contains 346308 sequences. (Running on oeis4.)