[seqfan] Is this sequence interesting?

[Andrew Weimholt]

Smallest unused number such that for any prime p, (p+1)|a(n) implies p|a(n+1)

1, 2, 3, 4, 6, 10, 5, 7, 8, 21, 9, 12, 330, 31610, 11, 13, 14, 26, 15,
16, 42, 5330, 409, 17, 18, 170, 19, 20, 57, 22, 23, 24, 7590,
7526015322170, 2462247386861400614203033, 25, 27, 28, 39, 29, 30, 290,
31, 32, 651, 34, 33, 36, 5610, 606139356770,
4471670685645331592970549159770045950729, 35, 37, 38, 74, 73, 40, 399,
44, 129, 41, 43, 45, 46, 47, 48, 2497110,
18357856193046830514707003334732167656898967581695292011731472733408286953690,

Not sure what the next term is, but the term after the next is 49.

Andrew