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 A129314 #11 Nov 12 2022 02:14:29
%S A129314 1,2,6,12,24,30,42,54,60,66,90,132,138,210,270,300,318,342,390,420,
%T A129314 450,624,690,696,750,798,924,930,1170,1224,1326,1362,1428,1434,1500
%N A129314 Records in A127356.
%e A129314 As can be gathered from A127356, the first six records are A127356(1) = 1, A127356(2) = 2, A127356(3) = 6, A127356(10) = 12, A127356(13) = 24, A127356(77) = 30. Hence a(1) to a(6) are 1, 2, 6, 12, 24, 30.
%t A129314 sk[n_]:=Module[{k=2},While[!PrimeQ[n+k^2],k=k+2];k];DeleteDuplicates[ Join[ {1},Table[sk[n],{n,Prime[Range[2,1000000]]}]],GreaterEqual] (* The program generates the first 22 terms of the sequence. *) (* _Harvey P. Dale_, Nov 07 2022 *)
%o A129314 (Python)
%o A129314 from itertools import count, islice
%o A129314 from sympy import isprime, nextprime, prime
%o A129314 def agen():
%o A129314 pn = 2; record = 1; yield record
%o A129314 for n in count(2):
%o A129314 k, pn = 2, nextprime(pn)
%o A129314 while not isprime(pn + k*k): k += 2
%o A129314 if k > record: record = k; yield record
%o A129314 print(list(islice(agen(), 20))) # _Michael S. Branicky_, Nov 11 2022
%Y A129314 Cf. A127356, A129315 (where records occur).
%K A129314 nonn,more
%O A129314 1,2
%A A129314 _Klaus Brockhaus_, Apr 09 2007
%E A129314 a(27)-a(33) from _Donovan Johnson_, Dec 09 2008
%E A129314 a(34)-a(35) from _Michael S. Branicky_, Nov 11 2022