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A061214
Product of composite numbers between the n-th and (n+1)st primes.
19
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
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. A046933 and A054265 (number and sum of these composites).
Sequence in context: A027717 A035481 A323214 * A137024 A054264 A077305
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