This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A382051 #23 Apr 08 2025 10:20:03
%S A382051 11,17,23,29,37,53,59,67,79,89,97,127,137,149,157,163,173,179,191,211,
%T A382051 223,239,251,257,263,269,277,293,307,331,347,367,397,409,419,431,457,
%U A382051 479,487,499,521,541,557,587,631,641,673,691,701,709,719,727,751,769,787,797
%N A382051 Primes prime(k) such that k*log(k)/prime(k) < (k-1)*log(k-1)/prime(k-1).
%C A382051 a(n) ~ prime(round(n*e)) as n tends to infinity, where e is Euler's number.
%F A382051 Limit_{n->oo} n / PrimePi(a(n)) = 1/e.
%e A382051 11 is a term because 5*log(5)/11 < 4*log(4)/7 and 11 is the 5th prime following 7.
%e A382051 17 is a term because 7*log(7)/17 < 6*log(6)/13 and 17 is the 7th prime following 13.
%t A382051 Select[Prime[Range[2,139]],PrimePi[#]*Log[PrimePi[#]]/#<(PrimePi[#]-1)*Log[PrimePi[#]-1]/NextPrime[#,-1]&] (* _James C. McMahon_, Apr 08 2025 *)
%o A382051 (PARI) my(N=1); forprime(P=3, 800, my(Q=precprime(P-1), AR0=N*log(N)/Q, AR=(N+1)*log(N+1)/P); N++; if(AR<AR0, print1(P,", ")));
%Y A382051 A subsequence is A060769.
%Y A382051 Cf. A382052, A060769, A001113, A068985.
%K A382051 nonn
%O A382051 1,1
%A A382051 _Alain Rocchelli_, Mar 13 2025