Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #14 Dec 31 2018 03:50:45
%S 15,33,91,213,213,893,893,1343
%N Start of first occurrence of n consecutive odd squarefree composite numbers.
%C The sequence is finite because among 9 or more consecutive odd numbers there is always a multiple of 3*3. - _Rémy Sigrist_, Dec 19 2018
%e a(1) = 15 = A024556(1).
%e a(2) = 33 because 33 = 3*11 and 35 = 5*7 is the smallest pair of odd squarefree composite numbers. 31 and 37 are prime.
%e a(8) = 1343: 1343=17*79, 1345=5*269, 1347=3*449, 1349=19*71, 1351=7*193, 1353=3*11*41, 1355=5*271, 1357=23*59, whereas 1341=3^2*149 and 1359=3^2*151 are not squarefree.
%t a[n_] := For[k = 1, True, k = k+2, If[AllTrue[Range[k, k+2(n-1), 2], CompositeQ[#] && SquareFreeQ[#]&], Return[k]]];
%t Array[a, 8] (* _Jean-François Alcover_, Dec 31 2018 *)
%Y Cf. A024556, A321617.
%K nonn,fini,full
%O 1,1
%A _Hugo Pfoertner_, Dec 19 2018