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
Keywords
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
Programs
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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 *)