A322493 Start of first occurrence of n consecutive odd squarefree composite numbers.

15, 33, 91, 213, 213, 893, 893, 1343

Offset: 1

Author

Hugo Pfoertner, Dec 19 2018

Keywords

• nonn
• fini
• full

Comments

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

Examples

			a(1) = 15 = A024556(1).
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.
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.
		

Crossrefs

Cf. A024556, A321617.

Programs

Mathematica

a[n_] := For[k = 1, True, k = k+2, If[AllTrue[Range[k, k+2(n-1), 2], CompositeQ[#] && SquareFreeQ[#]&], Return[k]]];
Array[a, 8] (* Jean-François Alcover, Dec 31 2018 *)