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A272899 Product of next n prime numbers greater than n. 0
2, 15, 385, 5005, 323323, 7436429, 955049953, 35336848261, 1448810778701, 62298863484143, 14107860812636383, 832363787945546597, 261682369333342226303, 18579448222667298067513, 1356299720254712758928449, 107147677900122307955347471 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

Table of n, a(n) for n=1..16.

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(1) = 2 = 2.

a(2) = 3 * 5 = 15.

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

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

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

STATUS

approved

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Last modified May 16 13:57 EDT 2021. Contains 343947 sequences. (Running on oeis4.)