A358898 - OEIS

%I #6 Dec 15 2022 14:01:08

%S 199,523,1669,1933,1951,2113,2311,2593,2803,2971,3469,4159,4423,6451,

%T 7129,7351,7459,7759,8389,8971,9439,10009,10039,10531,11551,12073,

%U 12163,13009,13339,13933,14251,14563,14593,15683,16141,16453,17209,17683,17989,18919

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

%e 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.

%t p[n_] := Prime[n];

%t u = Select[1 + Range[3000], p[#]^p[#] < p[# + 1]^p[# - 1] &] (* A358897 *)

%t Prime[u]  (* A358898 *)

%Y Cf. A000040, A053089, A358897.

%K nonn

%O 1,1

%A _Clark Kimberling_, Dec 06 2022