A358898 Primes p(k) such that p(k)^p(k) < p(k+1)^p(k-1).

199, 523, 1669, 1933, 1951, 2113, 2311, 2593, 2803, 2971, 3469, 4159, 4423, 6451, 7129, 7351, 7459, 7759, 8389, 8971, 9439, 10009, 10039, 10531, 11551, 12073, 12163, 13009, 13339, 13933, 14251, 14563, 14593, 15683, 16141, 16453, 17209, 17683, 17989, 18919

Offset: 1

Author

Clark Kimberling, Dec 06 2022

Keywords

• nonn

Examples

			For k=46, let p = prime(45) = 197, q = prime(46) = 199, and r = prime(47) = 211.  Then q^q < r^p, where (r^p) = (2.5815...)*q^q.
		

Crossrefs

Cf. A000040, A053089, A358897.

Programs

Mathematica

p[n_] := Prime[n];
u = Select[1 + Range[3000], p[#]^p[#] < p[# + 1]^p[# - 1] &] (* A358897 *)
Prime[u]  (* A358898 *)