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Numbers k such that p(k)^p(k) < p(k+1)^p(k-1), where p(k) = prime(k).
2

%I #6 Dec 15 2022 14:00:53

%S 46,99,263,295,297,319,344,378,409,429,487,573,602,838,914,937,945,

%T 985,1051,1116,1170,1231,1233,1288,1392,1446,1457,1551,1585,1648,1675,

%U 1708,1710,1831,1879,1908,1983,2032,2064,2154,2176,2250,2310,2327,2344,2524

%N Numbers k such that p(k)^p(k) < p(k+1)^p(k-1), where p(k) = prime(k).

%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, A358898.

%K nonn

%O 1,1

%A _Clark Kimberling_, Dec 06 2022