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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.
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%I #17 Aug 10 2024 03:54:39

%S 0,2,19,163,1966,26781,468178,9053660,210809338,6169323433,

%T 192531847119,7161249384065,294835346718114,12720163581273289,

%U 599492054060678551,31846920298131321838,1882691381652701947175,115037118886354670022443,7718754971134321663159676

%N 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.

%F a(n) = A002110(n) - A000849(n) - 1. - _Amiram Eldar_, Aug 09 2024

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

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

%o (PARI) a(n) = my(m = vecprod(primes(n))); m - primepi(m) - 1; \\ _Amiram Eldar_, Aug 09 2024

%Y Cf. A000720, A002808, A002110, A000849.

%K nonn

%O 1,2

%A _Labos Elemer_, Nov 28 2001

%E More terms from _Robert G. Wilson v_, Nov 29 2001

%E Name clarified and a(13)-a(19) calculated from the data at A000849 and added by _Amiram Eldar_, Aug 09 2024