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 A240339 #15 Sep 27 2024 07:48:00
%S A240339 59,97,1321,1621,2539,3511,4339,4889,5591,6491,6917,9419,10289,11689,
%T A240339 16381,18719,19441,23053,23567,28499,41051,47143,64661,65203,67939,
%U A240339 71023,82493,89107,94999,98927,106087,114941,117281,120823,135647,139361,144289,154799
%N A240339 Primes p which are floor of Root-Mean-Cube (RMC) of prime(n) and prime(n+1).
%H A240339 Georg Fischer, <a href="/A240339/b240339.txt">Table of n, a(n) for n = 1..1700</a> (first 357 terms from K. D. Bajpai)
%e A240339 13 and 17 are consecutive primes: sqrt((13^3 + 17^3)/2) = 59.62382073: floor(59.62382073)= 59, which is prime and appears in the sequence.
%e A240339 19 and 23 are consecutive primes: sqrt((19^3 + 23^3)/2) = 97.53460923: floor(97.53460923)= 97, which is prime and appears in the sequence.
%p A240339 select(isprime, {seq(floor(sqrt((ithprime(n)^3 + ithprime(n+1)^3)/2)),n=1..1000)}); # corrected by _Georg Fischer_, Sep 27 2024
%t A240339 Select[Floor[Sqrt[Mean[#]]]&/@(Partition[Prime[Range[600]],2,1]^3), PrimeQ] (* _Harvey P. Dale_, Sep 24 2014 *)
%Y A240339 Cf. A000040, A075471, A088165, A239941.
%K A240339 nonn
%O A240339 1,1
%A A240339 _K. D. Bajpai_, Apr 04 2014