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

1,1

Links

Table of n, a(n) for n=1..37.

Example

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.

Sequence in context: A358356 A368800 A039020 * A055742 A263041 A216888

Adjacent sequences: A379446 A379447 A379448 * A379450 A379451 A379452

Keyword

nonn,more

Author

Jean-Marc Rebert, Dec 23 2024

Extensions

a(37) from Jinyuan Wang, Dec 23 2024

Status

approved