cp's OEIS Frontend

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.

%I A283668 #24 Sep 08 2022 08:46:19
%S A283668 1,3,6,11,22,25,31,35,36,39,49,51,58,65,67,69,81,85,86,92,97,99,100,
%T A283668 110,115,119,125,126,133,135,142,144,149,150,153,161,164,165,167,169,
%U A283668 172,174,175,176,186,194,199,201,206,208,210,214,217,224,231,235,236,239,240,242,244,247,251
%N 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.
%F A283668 a(n) = A283628(9n) = A283628(9n-1) + 1 = A283628(9n+1) - 1.
%F A283668 a(n) ~ k*n where k = Product_{ p prime > 3} p^2/(p^2 - 12) = 3.7192316.... - _Michael R Peake_, Mar 16 2017
%e A283668 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.
%t A283668 Select[Range@ 256, Function[n, Times @@ Boole@ Map[SquareFreeQ, 36 n + Flatten@ {-#, #} &@ Drop[Range@ 7, {4}]] == 1]] (* _Michael De Vlieger_, Mar 13 2017 *)
%o A283668 (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) ];
%o A283668 (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;
%o A283668 for(n=1, 251, if(isok(n), print1(n,", "))) \\ _Indranil Ghosh_, Mar 13 2017
%Y A283668 Cf. A005117, A283628.
%K A283668 nonn
%O A283668 1,2
%A A283668 _Juri-Stepan Gerasimov_, Mar 13 2017