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 A297960 #50 Apr 11 2021 11:59:10
%S A297960 4,9,30,49,99,74,101,71,72,35,28,9,4
%N A297960 a(1) = number of 1-digit primes (that is, 4: 2,3,5,7); then a(n) = number of distinct n-digit prime numbers obtained by alternately right- and left-concatenating a digit to the a(n-1) primes obtained in the previous iteration.
%C A297960 No 14-digit numbers can be obtained from the four 13-digit numbers counted by a(13).
%e A297960 1-digit 2-digit 3-digit 4-digit ... 13-digit
%e A297960 ------------------------------------------------------------
%e A297960 2 23 223 2237
%e A297960 2239
%e A297960 523 5231
%e A297960 5233
%e A297960 5237
%e A297960 823 8231
%e A297960 8233 6638182333331
%e A297960 8237
%e A297960 29 229 2293
%e A297960 2297
%e A297960 829 8291
%e A297960 8293
%e A297960 8297
%e A297960 929 9293
%e A297960 3 31 131 1319
%e A297960 331 3313
%e A297960 3319
%e A297960 431
%e A297960 631 6311 5981563119937
%e A297960 6317
%e A297960 37 137 1373
%e A297960 337 3371
%e A297960 3373
%e A297960 937 9371
%e A297960 9377
%e A297960 5 53 353 3533
%e A297960 3539
%e A297960 653
%e A297960 853 8537
%e A297960 8539
%e A297960 953 9533
%e A297960 9539
%e A297960 59 359 3593
%e A297960 659 6599
%e A297960 859 8597
%e A297960 8599
%e A297960 7 71 271 2711
%e A297960 2713
%e A297960 2719
%e A297960 571 5711
%e A297960 5717
%e A297960 971 9719
%e A297960 73 173 1733
%e A297960 373 3733
%e A297960 3739
%e A297960 673 6733 8313667333393
%e A297960 6737
%e A297960 773
%e A297960 79 179
%e A297960 379 3793 2682637937713
%e A297960 3797
%e A297960 479 4793
%e A297960 4799
%e A297960 ------------------------------------------------------------
%e A297960 a(1) = 4, a(2) = 9, a(3) = 30, a(4) = 49, ..., a(13) = 4.
%t A297960 Block[{b = 10, t}, t = Select[Range[b], CoprimeQ[#, b] &]; TakeWhile[Length /@ Fold[Function[{a, n}, Append[a, If[OddQ[n], Join @@ Map[Function[k, Select[Map[Prepend[k, #] &, Range[9]], PrimeQ@ FromDigits[#, b] &]], Last[a]], Join @@ Map[Function[k, Select[Map[Append[k, #] &, t], PrimeQ@ FromDigits[#, b] &]], Last[a]]]]] @@ {#1, #2} &, {IntegerDigits[Prime@ Range@ PrimePi@b, b]}, Range[2, 16]], # > 0 &]] (* _Michael De Vlieger_, Jan 20 2018 *)
%o A297960 (Python)
%o A297960 from sympy import isprime
%o A297960 def alst():
%o A297960 primes, alst = [2, 3, 5, 7], []
%o A297960 while len(primes) > 0:
%o A297960 alst.append(len(primes))
%o A297960 if len(alst)%2 == 0:
%o A297960 candidates = set(int(d+str(p)) for p in primes for d in "123456789")
%o A297960 else:
%o A297960 candidates = set(int(str(p)+d) for p in primes for d in "1379")
%o A297960 primes = [c for c in candidates if isprime(c)]
%o A297960 return alst
%o A297960 print(alst()) # _Michael S. Branicky_, Apr 11 2021
%Y A297960 Cf. A050986, A050987, A297961, A298048.
%K A297960 nonn,full,base,fini
%O A297960 1,1
%A A297960 _Seiichi Manyama_, Jan 09 2018