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 A061216 a(n) = product of all even numbers between n-th prime and (n+1)-st prime. 1
 1, 4, 6, 80, 12, 224, 18, 440, 17472, 30, 39168, 1520, 42, 2024, 124800, 175392, 60, 261888, 4760, 72, 438672, 6560, 635712, 74718720, 9800, 102, 11024, 108, 12320, 356925975275520, 16640, 2405568, 138, 61857653760, 150, 3651648, 4095360 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Previous name used "even composite numbers", but if an even number is strictly between two primes, it is composite. So the word 'composite' isn't needed in the title. - David A. Corneth, Aug 21 2016 LINKS Harry J. Smith, Table of n, a(n) for n = 1..2000 FORMULA a(n) = 2^((prime(n+1)-prime(n))/2) * ((prime(n+1)-1)/2)!/(prime(n)-1)/2)! for n >= 2. - Robert Israel, Aug 28 2016 EXAMPLE a(4) = 80 = 8 * 10, as 7 is the 4th prime and 11 is the 5th prime. a(9) = 17472. Let p_(n) = prime(n). p_(9) = 23, p_(10) = 29. The number of even numbers between 23 and 29 is floor((29 - 23) / 2) = 3. So a(9) is 2^3 * (23 + 1)/2 * ... * (29 - 1)/2 = 17472. - David A. Corneth, Aug 21 2016 MAPLE f:= proc(n) local p, q; p:= ithprime(n); q:= ithprime(n+1); 2^((q-p)/2)*floor(q/2)!/floor(p/2)! end proc: f(1):= 1: map(f, [\$1..100]); # Robert Israel, Aug 28 2016 MATHEMATICA f[n_]:=Module[{pn=Prime[n], pn1=Prime[n+1]}, Times@@Range[pn+1, pn1, 2]]; Table[f[i], {i, 45}] (* Harvey P. Dale, Jan 16 2011 *) PROG (PARI) for(n=1, 50, p=1; for(k=prime(n)+1, prime(n+1)-1, if(k%2==0, p=p*k)); print1(p", ")) (PARI) n=0; q=2; forprime (p=3, prime(2001), a=1; for (i=q + 1, p - 1, if (i%2==0, a*=i)); q=p; write("b061216.txt", n++, " ", a) ) \\ Harry J. Smith, Jul 19 2009 (PARI) a(n) = {my(p1 = prime(n), p2 = nextprime(p1 + 1)); 2^((p2-p1)\2) * prod(i=(p1+1)\2, (p2-1)\2, i)} \\ David A. Corneth, Aug 21 2016 CROSSREFS Cf. A061214, A061215. Sequence in context: A013128 A012971 A197315 * A058163 A303211 A264374 Adjacent sequences: A061213 A061214 A061215 * A061217 A061218 A061219 KEYWORD nonn AUTHOR Amarnath Murthy, Apr 22 2001 EXTENSIONS Corrected and extended by Ralf Stephan, Mar 22 2003 Name simplified by David A. Corneth, Aug 21 2016 STATUS approved

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Last modified August 9 16:51 EDT 2024. Contains 375044 sequences. (Running on oeis4.)