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 A385210 #21 Jun 22 2025 09:39:38
%S A385210 1,1,2,2,3,3,5,2,5,5,4,5,8,3,5,4,7,7,8,7,8,8,7,6,5,11,8,9,8,3,6,6,5,3,
%T A385210 7,10,10,7,8,9,5,6,7,8,6,8,6,12,5,11,10,14,8,7,8,8,7,6,6,9,9,11,8,10,
%U A385210 10,9,12,8,8,8,6,9,11,11,7,13,5,11,5,9,10,9,9,7,8
%N A385210 Number of integers k such that prime(n) + primorial(k) is prime.
%e A385210 For prime(n=3): 5 + 2 = 7, 5 + 6 = 11, and 5 + any higher primorial will be composite, so a(3) = 2.
%t A385210 nn = 120; MapIndexed[Set[P[First[#2] - 1], #1] &, FoldList[Times, 1, Prime@ Range[nn]]]; Table[q = Prime[n]; Total@ Array[Boole@ PrimeQ[q + P[# - 1]] &, n], {n, nn}] (* _Michael De Vlieger_, Jun 22 2025 *)
%o A385210 (PARI) pri(n) = vecprod(primes(n)); \\ A002110
%o A385210 a(n) = my(nb=0, p=prime(n)); for (k=0, n-1, if (isprime(p+pri(k)), nb++);); nb; \\ _Michel Marcus_, Jun 21 2025
%Y A385210 Cf. A000040, A002110.
%K A385210 nonn
%O A385210 1,3
%A A385210 _Daniel D Gibson_, Jun 21 2025
%E A385210 More terms from _Michel Marcus_, Jun 21 2025