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A272899 Product of next n prime numbers greater than n.

%I A272899 #30 Jun 24 2024 18:26:42
%S A272899 1,2,15,385,5005,323323,7436429,955049953,35336848261,1448810778701,
%T A272899 62298863484143,14107860812636383,832363787945546597,
%U A272899 261682369333342226303,18579448222667298067513,1356299720254712758928449,107147677900122307955347471,46558817449894322874479515781
%N A272899 Product of next n prime numbers greater than n.
%C A272899 a(n) is of comparable size to n^n. - _Charles R Greathouse IV_, May 09 2016
%C A272899 a(n) is the product of the terms of the n-th row of A084754. - _Michel Marcus_, May 09 2016
%H A272899 Alois P. Heinz, <a href="/A272899/b272899.txt">Table of n, a(n) for n = 0..322</a>
%F A272899 a(n) = A002110(n + A000720(n))/A034386(n), where A002110(n) are the primorials, A000720(n) is the pi(n) prime counting function, and A034386(n) is the primorial of primes less than or equal to n. E.g., a(7) = 955049953 = A002110(11) / A034386(7).
%e A272899 a(0) = 1 (the empty product).
%e A272899 a(1) = 2 = 2.
%e A272899 a(2) = 3 * 5 = 15.
%e A272899 a(3) = 5 * 7 * 11 = 385.
%e A272899 a(4) = 5 * 7 * 11 * 13 = 5005.
%p A272899 a:= n-> mul((nextprime@@i)(n), i=1..n):
%p A272899 seq(a(n), n=0..17);  # _Alois P. Heinz_, Jun 24 2024
%t A272899 Table[Times@@Prime[Range[PrimePi[n] + 1, PrimePi[n] + n]], {n, 25}] (* _Alonso del Arte_, May 09 2016 *)
%o A272899 (PARI) a(n)=my(v=primes(primepi(n)+n)); prod(i=0,n-1,v[#v-i]) \\ _Charles R Greathouse IV_, May 09 2016
%o A272899 (Python)
%o A272899 from math import prod
%o A272899 from sympy import prime, primepi
%o A272899 def a(n): r = primepi(n); return prod(prime(i) for i in range(r+1, r+n+1))
%o A272899 print([a(n) for n in range(1, 17)]) # _Michael S. Branicky_, Feb 15 2021
%Y A272899 Cf. A000720, A002110, A007918, A034386, A084754.
%K A272899 nonn,easy
%O A272899 0,2
%A A272899 _Matthew Goers_, May 09 2016
%E A272899 a(0)=1 prepended by _Alois P. Heinz_, Jun 24 2024