A061214 Product of composite numbers between the n-th and (n+1)st primes.

1, 4, 6, 720, 12, 3360, 18, 9240, 11793600, 30, 45239040, 59280, 42, 91080, 311875200, 549853920, 60, 1072431360, 328440, 72, 2533330800, 531360, 4701090240, 60072730099200, 970200, 102, 1157520, 108, 1367520, 1063186156509747740870400000, 2146560, 43191973440

Offset

1,2

Links

T. D. Noe, Table of n, a(n) for n = 1..2000

Formula

A006530(a(n)) = A052248(n) for n > 1. - Reinhard Zumkeller, Jun 22 2011

Example

a(4) = 8 * 9 * 10 = 720. 7 is the fourth prime and 11 is the fifth prime. a(5) = 12 as 11 and 13 both are primes.

Maple

A061214 := proc(n)
    local k ;
    product(k, k=ithprime(n)+1..ithprime(n+1)-1) ;
end proc: # R. J. Mathar, Apr 23 2013

Mathematica

Table[Times@@Range[Prime[n]+1, Prime[n+1]-1], {n, 30}] (* Harvey P. Dale, Jun 14 2011 *)
Times@@Range[#[[1]]+1, #[[2]]-1]&/@Partition[Prime[Range[40]], 2, 1] (* Harvey P. Dale, Apr 23 2022 *)

Prog

(PARI) { n=0; q=2; forprime (p=3, prime(2001), a=1; for (i=q + 1, p - 1, a*=i); q=p; write("b061214.txt", n++, " ", a) ) } \\ Harry J. Smith, Jul 19 2009
(PARI) v=primes(100); for(i=1, #v-1, v[i]=prod(j=v[i]+1, v[i+1]-1, j)); vecextract(v, "1..-2") \\ Charles R Greathouse IV, Feb 27 2012
(Haskell)
a061214 n = a061214_list !! (n-1)
a061214_list = f a000040_list where
   f (p:ps'@(p':ps)) = (product [p+1..p'-1]) : f ps'
-- Reinhard Zumkeller, Jun 22 2011
(Python)
from math import prod
from sympy import prime
def A061214(n): return prod(i for i in range(prime(n)+1, prime(n+1))) # Chai Wah Wu, Jul 10 2022

Crossrefs

Cf. A006530, A052248, A052297, A072472, A361760, A361761.

Cf. A046933 and A054265 (number and sum of these composites).

Sequence in context: A027717 A035481 A323214 * A137024 A054264 A077305

Adjacent sequences: A061211 A061212 A061213 * A061215 A061216 A061217

Keyword

nonn

Author

Amarnath Murthy, Apr 21 2001

Extensions

More terms from James A. Sellers, Apr 24 2001

Better definition from T. D. Noe, Jan 21 2008

Status

approved