A362056 Prime numbers of the form prime(k)! - prime(k!).

3, 107, 4951, 39916141, 355687428046967

Offset

1,1

Comments

No other terms < prime(22)! - prime(22!) (using A062439).

Problem suggested by Carlos Rivera as a follow-on to Puzzle 1127 (see links).

Links

Table of n, a(n) for n=1..5.

Carlos Rivera, Puzzle 1127. Prime(11!)+Prime(11)!, The Prime Puzzles and Problems Connection.

Carlos Rivera, Puzzle 1128. Prime(n)!-Prime(n!), The Prime Puzzles and Problems Connection.

Formula

A261997(k) = A000142(A000040(k)) - A000040(A000142(k)) is in A000040.

Example

prime(2)! - prime(2!) = 3 is prime.
prime(3)! - prime(3!) = 107 is prime.
prime(4)! - prime(4!) = 4951 is prime.
prime(5)! - prime(5!) = 39916141 is prime.
prime(7)! - prime(7!) = 355687428046967 is prime.

Crossrefs

Cf. A000040, A000142, A062439.

Prime terms in A261997.

Sequence in context: A003705 A146214 A261997 * A061308 A302060 A336438

Adjacent sequences: A362053 A362054 A362055 * A362057 A362058 A362059

Keyword

nonn,hard,more

Author

Michael S. Branicky, Apr 06 2023

Status

approved