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 A376440 #9 Sep 24 2024 02:17:31
%S A376440 2,2,107,1657,25453,404819,1388449,137414987,402301129,87241770523
%N A376440 Smallest primes p_1 where products m of n consecutive primes p_1..p_n are such that only p_n > m^(1/n).
%e A376440 a(2) = 2 since m = 2*3 = 6 and 2 < sqrt(6).
%e A376440 a(3) = 2 since m = 2*3*5 = 30 and 3 < 30^(1/3).
%e A376440 a(4) = 107 since m = 107 * 109 * 113 * 127 = 167375713 and 113 < 167375713^(1/4), etc.
%t A376440 k = 1; Table[r = Range[0, n - 1]; While[(Set[{p, q, m}, {#[[1]], #[[-2]], Times @@ #}]; q > Surd[m, n]) &[Prime[k + r]], k++]; p, {n, 2, 6}]
%o A376440 (PARI) a(n) = {my(ps = vector(n, k, prime(k))); forprime(p = prime(n+1), , if(ps[#ps-1]^n < vecprod(ps), return(ps[1])); ps = concat(vecextract(ps, "^1"), p));} \\ _Amiram Eldar_, Sep 23 2024
%Y A376440 Cf. A374873.
%K A376440 nonn,hard,more
%O A376440 2,1
%A A376440 _Michael De Vlieger_, Sep 22 2024
%E A376440 a(10)-a(11) from _Amiram Eldar_, Sep 23 2024