A379449 Numbers k such that the prime gap between the consecutive primes p1 < k! = factorial(k) < p2 sets a new record.
3, 4, 5, 8, 13, 19, 24, 29, 34, 45, 47, 51, 56, 61, 71, 107, 127, 140, 184, 192, 198, 274, 284, 375, 384, 559, 592, 630, 689, 774, 792, 834, 1133, 1213, 1241, 1315, 1947
Offset: 1
Examples
a(1) = 3, because the prime gap between the consecutive primes 5 < 3! < 7 sets the first record of 2. n gap p1 < x! < p2 1 2 5 < 3! < 7; 2 6 23 < 4! < 29; 3 14 113 < 5! < 127; 4 54 40289 < 8! < 40343; 5 90 6227020777 < 13! < 6227020867; 6 190 121645100408831899 < 19! < 121645100408832089; 7 204 620448401733239439359927 < 24! < 620448401733239439360131;
Extensions
a(37) from Jinyuan Wang, Dec 23 2024