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a(n) is the least prime > prime(n)^prime(n).
2

%I #13 Mar 27 2024 15:42:33

%S 5,29,3137,823547,285311670673,302875106592269,827240261886336764251,

%T 1978419655660313589123997,20880467999847912034355032910581,

%U 2567686153161211134561828214731016126483589,17069174130723235958610643029059314756044734489,10555134955777783414078330085995832946127396083370199442559

%N a(n) is the least prime > prime(n)^prime(n).

%t NextPrime[#^#] & [Prime[Range[15]]] (* _Paolo Xausa_, Mar 27 2024 *)

%o (PARI) a371347(n) = nextprime(prime(n)^prime(n))

%o (Python)

%o from sympy import nextprime, prime

%o def A371347(n): return nextprime((m:=prime(n))**m) # _Chai Wah Wu_, Mar 27 2024

%Y Cf. A051674, A371346.

%K nonn

%O 1,1

%A _Hugo Pfoertner_, Mar 27 2024