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

Author

Jean-Marc Rebert, Dec 23 2024

Keywords

• nonn
• more

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;
		

Crossrefs

Cf. A054588, A350100, A378429.

Extensions

a(37) from Jinyuan Wang, Dec 23 2024