A272899 Product of next n prime numbers greater than n.

1, 2, 15, 385, 5005, 323323, 7436429, 955049953, 35336848261, 1448810778701, 62298863484143, 14107860812636383, 832363787945546597, 261682369333342226303, 18579448222667298067513, 1356299720254712758928449, 107147677900122307955347471, 46558817449894322874479515781

Offset

0,2

Comments

a(n) is of comparable size to n^n. - Charles R Greathouse IV, May 09 2016

a(n) is the product of the terms of the n-th row of A084754. - Michel Marcus, May 09 2016

Links

Alois P. Heinz, Table of n, a(n) for n = 0..322

Formula

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).

Example

a(0) = 1 (the empty product).
a(1) = 2 = 2.
a(2) = 3 * 5 = 15.
a(3) = 5 * 7 * 11 = 385.
a(4) = 5 * 7 * 11 * 13 = 5005.

Maple

a:= n-> mul((nextprime@@i)(n), i=1..n):
seq(a(n), n=0..17);  # Alois P. Heinz, Jun 24 2024

Mathematica

Table[Times@@Prime[Range[PrimePi[n] + 1, PrimePi[n] + n]], {n, 25}] (* Alonso del Arte, May 09 2016 *)

Prog

(PARI) a(n)=my(v=primes(primepi(n)+n)); prod(i=0, n-1, v[#v-i]) \\ Charles R Greathouse IV, May 09 2016
(Python)
from math import prod
from sympy import prime, primepi
def a(n): r = primepi(n); return prod(prime(i) for i in range(r+1, r+n+1))
print([a(n) for n in range(1, 17)]) # Michael S. Branicky, Feb 15 2021

Crossrefs

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

Sequence in context: A215743 A254224 A071102 * A060381 A256369 A145328

Adjacent sequences: A272896 A272897 A272898 * A272900 A272901 A272902

Keyword

nonn,easy

Author

Matthew Goers, May 09 2016

Extensions

a(0)=1 prepended by Alois P. Heinz, Jun 24 2024

Status

approved