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 A359406 #58 Feb 14 2023 02:35:43
%S A359406 1,2,3,23,43,141
%N A359406 Integers k such that the concatenation of k consecutive primes starting at 31 is prime.
%C A359406 The corresponding primes (p) known (31, 3137, 313741, ...) have an even number of digits and p (mod 10) == 1|7. For those at a(1)...a(6), p (mod 3) == p (mod 5) holds.
%C A359406 a(7): 3472 corresponds to a 15968-digit probable prime (certification in progress).
%C A359406 For a(8), k > 15000 (if it exists).
%C A359406 a(8) > 30000. - _Tyler Busby_, Feb 13 2023
%e A359406 2 is a term because the consecutive primes 31 and 37 concatenated to 3137 yield another prime.
%t A359406 UpToK[k_] := Block[{a := FromDigits @ Flatten @ IntegerDigits @ Join[{}, Prime @ Range[11, i]]}, Reap[ Do[ If[ PrimeQ[a], Sow[i - 10], Sow[Nothing]], {i, k}]]][[2, 1]]; UpToK[3500] (* or *)
%t A359406 UpToK[k_] := Flatten @ Parallelize @ MapIndexed[ If[ PrimeQ[#1], #2, Nothing] &, DeleteCases[ FromDigits /@ Flatten /@ IntegerDigits @ Prime @ Range[11, Range[k]], 0]]; UpToK[3500]
%Y A359406 Cf. A069151, A309191, A030996, A280894.
%K A359406 nonn,base,more
%O A359406 1,2
%A A359406 _Mikk Heidemaa_, Dec 30 2022