%I #8 Dec 17 2022 13:42:59
%S 2,3,5,29,137,179,197,239,281,521,617,659,1667,1931,1949,2111,2309,
%T 2591,2801,2969,3119,3371,3389,3467,4157,4421,5021,5279,5879,6449,
%U 6761,7127,7331,7349,7457,7757,8387,8969,9437,9547,10007,10037,10529,11549,12071
%N Primes p(k) such that p(k)^p(k + 1) < p(k + 2)^p(k).
%H Harvey P. Dale, <a href="/A358896/b358896.txt">Table of n, a(n) for n = 1..1000</a>
%e For k = 3, we have 5^7 = p(3)^p(4) < p(5)^p(3) = 11^5.
%t p[n_] := Prime[n];
%t u = Select[Range[3000], p[#]^p[# + 1] < p[# + 2]^p[#] &] (* A358895 *)
%t Prime[u] (* A358896 *)
%t Select[Partition[Prime[Range[1500]],3,1],#[[1]]^#[[2]]<#[[3]]^#[[1]]&][[All,1]] (* _Harvey P. Dale_, Dec 17 2022 *)
%Y Cf. A000040, A053089, A358895.
%K nonn
%O 1,1
%A _Clark Kimberling_, Dec 06 2022