A272899 - OEIS

%I #30 Jun 24 2024 18:26:42

%S 1,2,15,385,5005,323323,7436429,955049953,35336848261,1448810778701,

%T 62298863484143,14107860812636383,832363787945546597,

%U 261682369333342226303,18579448222667298067513,1356299720254712758928449,107147677900122307955347471,46558817449894322874479515781

%N Product of next n prime numbers greater than n.

%C a(n) is of comparable size to n^n. - _Charles R Greathouse IV_, May 09 2016

%C a(n) is the product of the terms of the n-th row of A084754. - _Michel Marcus_, May 09 2016

%H Alois P. Heinz, <a href="/A272899/b272899.txt">Table of n, a(n) for n = 0..322</a>

%F 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 a(0) = 1 (the empty product).

%e a(1) = 2 = 2.

%e a(2) = 3 * 5 = 15.

%e a(3) = 5 * 7 * 11 = 385.

%e a(4) = 5 * 7 * 11 * 13 = 5005.

%p a:= n-> mul((nextprime@@i)(n), i=1..n):

%p seq(a(n), n=0..17);  # _Alois P. Heinz_, Jun 24 2024

%t Table[Times@@Prime[Range[PrimePi[n] + 1, PrimePi[n] + n]], {n, 25}] (* _Alonso del Arte_, May 09 2016 *)

%o (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 (Python)

%o from math import prod

%o from sympy import prime, primepi

%o def a(n): r = primepi(n); return prod(prime(i) for i in range(r+1, r+n+1))

%o print([a(n) for n in range(1, 17)]) # _Michael S. Branicky_, Feb 15 2021

%Y Cf. A000720, A002110, A007918, A034386, A084754.

%K nonn,easy

%O 0,2

%A _Matthew Goers_, May 09 2016

%E a(0)=1 prepended by _Alois P. Heinz_, Jun 24 2024