Increasing length runs of consecutive composite numbers (records).

Terms

a(0) =1a(1) =3a(2) =5a(3) =7a(4) =13a(5) =17a(6) =19a(7) =21a(8) =33a(9) =35a(10) =43a(11) =51a(12) =71a(13) =85a(14) =95a(15) =111a(16) =113a(17) =117a(18) =131a(19) =147a(20) =153a(21) =179a(22) =209a(23) =219a(24) =221a(25) =233a(26) =247a(27) =249a(28) =281a(29) =287