A378429 Numbers k such that the prime gap between the consecutive primes p1 < k# = primorial(k) < p2 sets a new record.

3, 7, 13, 17, 23, 29, 37, 43, 47, 61, 71, 79, 83, 97, 101, 109, 137, 193, 347, 349, 409, 457, 587, 599, 887, 929, 967, 1319, 1801, 1877, 2081, 2687, 2731, 2741, 2843, 2939, 2957, 3673, 3823, 4621, 5717, 6011, 6151, 6563, 6863, 7393, 8389, 9833, 11903, 12547

Offset

1,1

Links

Table of n, a(n) for n=1..50.

Example

a(1) = 3, because the prime gap between the consecutive primes 5 < 3# < 7 sets the first record of 2.
 n gap       p1        a(n)#        p2
 1   2             5 <   3# <             7
 2  12           199 <   7# <           211
 3  18         30029 <  13# <         30047
 4  48        510481 <  17# <        510529
 5  80     223092827 <  23# <     223092907
 6 102    6469693189 <  29# <    6469693291
 7 120 7420738134751 <  37# < 7420738134871

Crossrefs

Cf. A001223, A058044, A034386, A350100.

Sequence in context: A063226 A288709 A040106 * A191028 A034914 A034913

Adjacent sequences: A378426 A378427 A378428 * A378430 A378431 A378432

Keyword

nonn

Author

Jean-Marc Rebert, Dec 20 2024

Extensions

a(32)-a(39) from Amiram Eldar, Dec 20 2024

a(40)-a(50) from Michael S. Branicky, Dec 21 2024

Status

approved