A358900 Primes prime(k) such that prime(k)^prime(k) > prime(k-1)^prime(k+1).

5, 11, 29, 149, 1151, 1277, 1931, 1949, 2129, 2237, 2267, 2999, 3251, 3299, 3821, 4049, 4481, 4547, 4721, 5501, 6197, 6449, 6761, 6947, 8999, 9461, 9719, 10007, 10037, 10427, 10937, 11351, 11549, 11777, 12071, 13217, 13829, 13997, 14591, 15727, 16183, 17291

Offset: 1

Author

Clark Kimberling, Dec 06 2022

Keywords

• nonn

Examples

			For k = 3, we have prime(2) = 2, prime(3) = 5, prime(4) = 7, and 3125 = 5^5 > 3^7 = 2187.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..2000 (first 600 terms from Harvey P. Dale)

Crossrefs

Cf. A000040, A053089, A358899.

Programs

Mathematica

p[n_] := Prime[n];
u = Select[1 + Range[3000], p[#]^p[#] > p[# - 1]^p[# + 1] &]  (* A358899 *)
Prime[u]  (* A358900 *)
Select[Partition[Prime[Range[2000]],3,1],#[[2]]^#[[2]]>#[[1]]^#[[3]]&][[;;,2]] (* Harvey P. Dale, Oct 12 2023 *)