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 A359939 #10 Jan 21 2023 03:27:42
%S A359939 2,3,5,19,41,67,113,653,883,1439,3823,10631,12841,14251,23357,27103,
%T A359939 30491,64679,78823,110977,115127,118747,159431,215587,301039,342257,
%U A359939 343639,428401,473383,493583,566723,621133,638371,639157,680539,904049,993037,1146133,1252507
%N A359939 Lexicographically earliest strictly increasing sequence of primes whose partial products lie between noncomposite numbers.
%H A359939 Amiram Eldar, <a href="/A359939/b359939.txt">Table of n, a(n) for n = 1..150</a>
%e A359939 2 - 1 = 1 and 2 + 1 = 3 are both noncomposite numbers.
%e A359939 2*3 - 1 = 5 and 2*3 + 1 = 7 are both noncomposite numbers.
%e A359939 2*3*5 - 1 = 29 and 2*3*5 + 1 = 31 are both noncomposite numbers.
%t A359939 a[1] = 2; a[n_] := a[n] = Module[{r = Product[a[k],{k, 1, n-1}], p = NextPrime[a[n-1]]}, While[!PrimeQ[r*p-1] || !PrimeQ[r*p+1], p = NextPrime[p]]; p]; Array[a, 50]
%Y A359939 Cf. A008578, A014574, A039726, A087898, A167777, A359940.
%K A359939 nonn
%O A359939 1,1
%A A359939 _Amiram Eldar_, Jan 19 2023