A358896 Primes p(k) such that p(k)^p(k + 1) < p(k + 2)^p(k).

2, 3, 5, 29, 137, 179, 197, 239, 281, 521, 617, 659, 1667, 1931, 1949, 2111, 2309, 2591, 2801, 2969, 3119, 3371, 3389, 3467, 4157, 4421, 5021, 5279, 5879, 6449, 6761, 7127, 7331, 7349, 7457, 7757, 8387, 8969, 9437, 9547, 10007, 10037, 10529, 11549, 12071

Offset: 1

Author

Clark Kimberling, Dec 06 2022

Keywords

• nonn

Examples

			For k = 3, we have 5^7 = p(3)^p(4) < p(5)^p(3) = 11^5.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A053089, A358895.

Programs

Mathematica

p[n_] := Prime[n];
u = Select[Range[3000], p[#]^p[# + 1] < p[# + 2]^p[#] &]  (* A358895 *)
Prime[u]  (* A358896 *)
Select[Partition[Prime[Range[1500]],3,1],#[[1]]^#[[2]]<#[[3]]^#[[1]]&][[All,1]] (* Harvey P. Dale, Dec 17 2022 *)