A065898 Which composite number is the product of first n primes (the n-th primorial number)?: a(n) = k such that A002808(k) = A002110(n), or 0 if A002110(n) is not composite.

0, 2, 19, 163, 1966, 26781, 468178, 9053660, 210809338, 6169323433, 192531847119, 7161249384065, 294835346718114, 12720163581273289, 599492054060678551, 31846920298131321838, 1882691381652701947175, 115037118886354670022443, 7718754971134321663159676

Offset: 1

Author

Labos Elemer, Nov 28 2001

Keywords

• nonn

Examples

			a(3) = 19 because 2*3*5 = 30 = A002808(19) is the 19th composite number.
		

Crossrefs

Cf. A000720, A002808, A002110, A000849.

Programs

Mathematica

Table[q = Product[ Prime[i], {i, 1, n}]; q - PrimePi[q] - 1, {n, 1, 12}]

PARI

a(n) = my(m = vecprod(primes(n))); m - primepi(m) - 1; \\ Amiram Eldar, Aug 09 2024

Formula

a(n) = A002110(n) - A000849(n) - 1. - Amiram Eldar, Aug 09 2024

Extensions

More terms from Robert G. Wilson v, Nov 29 2001

Name clarified and a(13)-a(19) calculated from the data at A000849 and added by Amiram Eldar, Aug 09 2024