A362056 - OEIS

%I #17 Apr 15 2023 10:08:45

%S 3,107,4951,39916141,355687428046967

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

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

%C Problem suggested by _Carlos Rivera_ as a follow-on to Puzzle 1127 (see links).

%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_1127.htm">Puzzle 1127. Prime(11!)+Prime(11)!</a>, The Prime Puzzles and Problems Connection.

%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_1128.htm">Puzzle 1128. Prime(n)!-Prime(n!)</a>, The Prime Puzzles and Problems Connection.

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

%e prime(2)! - prime(2!) = 3 is prime.

%e prime(3)! - prime(3!) = 107 is prime.

%e prime(4)! - prime(4!) = 4951 is prime.

%e prime(5)! - prime(5!) = 39916141 is prime.

%e prime(7)! - prime(7!) = 355687428046967 is prime.

%Y Cf. A000040, A000142, A062439.

%Y Prime terms in A261997.

%K nonn,hard,more

%O 1,1

%A _Michael S. Branicky_, Apr 06 2023