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 A309191 #21 Jan 15 2025 12:15:11
%S A309191 2,2,31,4603,910307,352367441,23908162969,483148266971
%N A309191 a(n) is the least prime such that each concatenation of 1 <= k <= n consecutive primes beginning with a(n) is prime, or 0 if no such prime exists.
%H A309191 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_708.htm">Puzzle 708. Find sets of k consecutive primes such that ...</a>, The Prime Puzzles & Problems Connection.
%e A309191 a(2)=2; 2, 3 are 2 consecutive primes and their concatenation 23 is also prime.
%e A309191 a(3)=31 since 31, 37, and 41 are 3 consecutive primes and 3137 and 313741 are both prime.
%t A309191 a[n_] := Block[{p = Prime@ Range@ n}, While[! AllTrue[Range[2, n], PrimeQ@ FromDigits@ Flatten@ IntegerDigits@ Take[p, #] &], p = Append[ Rest@ p, NextPrime@ Last@ p]]; p[[1]]]; Array[a, 5] (* _Giovanni Resta_, Jul 16 2019 *)
%Y A309191 Cf. A030996.
%K A309191 nonn,base,more
%O A309191 1,1
%A A309191 _Jean-Marc Rebert_, Jul 16 2019