A385210 Number of integers k such that prime(n) + primorial(k) is prime.

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, 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, 10, 9, 12, 8, 8, 8, 6, 9, 11, 11, 7, 13, 5, 11, 5, 9, 10, 9, 9, 7, 8

Offset: 1

Author

Daniel D Gibson, Jun 21 2025

Keywords

• nonn

Examples

			For prime(n=3): 5 + 2 = 7, 5 + 6 = 11, and 5 + any higher primorial will be composite, so a(3) = 2.
		

Crossrefs

Cf. A000040, A002110.

Programs

Mathematica

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 *)

PARI

pri(n) = vecprod(primes(n)); \\ A002110
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

Extensions

More terms from Michel Marcus, Jun 21 2025