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%I #43 May 26 2015 18:30:34
%S 13,13,1263,837140
%N a(n) = smallest k such that none of 4*k - 4*j + 2 and 4*k + 4*j - 2, j = 0, 1, 2, .. n, are squarefree.
%C a(4) > 10^8.
%e a(0) = 13 because none of 4*13 - 4*0 + 2 = 54, 4*13 + 4*0 - 2 = 50 are squarefree,
%e a(1) = 13 because none of 4*13 - 4*1 + 2 = 50, 4*13 + 4*1 - 2 = 54 are squarefree,
%e a(2) = 1263 because none of 4*1263 - 4*2 + 2 = 5046, 4*1263 - 4*1 + 2 = 5050, 4*1263 + 4*1 - 2 = 5054, 4*1263 + 4*2 - 2 = 5058 are squarefree.
%t {1}~Join~Table[k = 0; While[! And[NoneTrue[4 k + 2 # & /@ Range@ n, SquareFreeQ], NoneTrue[4 k - 2 # & /@ Range@ n, SquareFreeQ]], k++]; k, {n, 6}] (* _Michael De Vlieger_, May 09 2015, Version 10 *)
%o (PARI) ok(n,k)=for(j=1,n, if(issquarefree(4*k-4*j+2) || issquarefree(4*k+4*j-2), return(0))); 1
%o a(n)=my(k); while(!ok(n,k++),); k \\ _Charles R Greathouse IV_, May 22 2015
%Y Cf. A257115.
%K nonn,more
%O 0,1
%A _Juri-Stepan Gerasimov_, May 03 2015
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