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 A355601 #8 Jan 31 2023 12:58:07
%S A355601 47,53,521,6037,3347,4931,105667,1131259,4739509,175166071,3834885547
%N A355601 a(1) = 47. For n > 1, a(n) = smallest prime q such that q^(a(n-1)-1) == 1 (mod a(n-1)^2).
%C A355601 Is this overall an increasing sequence or does it enter a cycle?
%C A355601 The sequence decreases for the first time at n = 5.
%t A355601 nxt[a_]:=Module[{q=3},While[PowerMod[q,a-1,a^2]!=1,q=NextPrime[q]];q]; NestList[ nxt,47,10] (* The program will take a long time to run. *) (* _Harvey P. Dale_, Jan 31 2023 *)
%o A355601 (PARI) seq(start, terms) = my(x=start, i=1); print1(start, ", "); while(1, forprime(q=1, , if(Mod(q, x^2)^(x-1)==1, print1(q, ", "); x=q; i++; if(i >= terms, break({2}), break))))
%o A355601 seq(47, 20) \\ Print initial 20 terms of sequence
%Y A355601 Row n = 15 of A249162.
%Y A355601 Cf. A355597, A355598, A355599, A355600, A355602.
%K A355601 nonn,hard,more
%O A355601 1,1
%A A355601 _Felix Fröhlich_, Jul 09 2022