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A238711 Product of all primes p such that 2n - p is also prime.

%I A238711 #15 Apr 27 2025 00:52:05
%S A238711 2,3,15,105,35,231,2145,5005,4641,53295,1616615,119301,21505,7436429,
%T A238711 21489,57998985,3038795305,4123,13844919,10393190665,12838371,
%U A238711 299859855,7292509103495,12023917269,70691995,37198413949697,62483343,2769282065,98755025688454681
%N A238711 Product of all primes p such that 2n - p is also prime.
%C A238711 Product of n-th row in triangle A171637;
%C A238711 All terms greater than 3 are odd, composite and squarefree numbers, cf. A024556.
%C A238711 n is prime iff n is a factor of a(n).
%C A238711 Product of the distinct primes in the Goldbach partitions of 2n. - _Wesley Ivan Hurt_, Sep 29 2020
%H A238711 Reinhard Zumkeller, <a href="/A238711/b238711.txt">Table of n, a(n) for n = 2..2000</a>
%F A238711 A020639(a(n)) = A020481(n); A006530(a(n)) = A020482(n);
%F A238711 A001221(a(n)) = A035026(n); A008472(a(n)) = A238778(n);
%F A238711 A027748(a(n),k) + A027748(a(n),l+1-k) = 2*n for k=1..l, with l=A001221(a(n)); particulary A020639(a(n))+A006530(a(n)) = 2*n;
%F A238711 a(n) = n^c(n) * Product_{i=1..n-1} (i*(2*n-i))^(c(i)*c(2*n-i)), where c is the prime characteristic (A010051). - _Wesley Ivan Hurt_, Sep 29 2020
%t A238711 Table[Times@@Select[Select[Prime[Range[2 n]], # < 2 n &], PrimeQ[2 n - #] &], {n, 2, 30}] (* _Robert Price_, Apr 26 2025 *)
%o A238711 (Haskell)
%o A238711 a238711 n = product $ filter ((== 1) . a010051') $
%o A238711    map (2 * n -) $ takeWhile (<= 2 * n) a000040_list
%Y A238711 Cf. A000040, A010051, A238778, subsequence of A056911.
%K A238711 nonn
%O A238711 2,1
%A A238711 _Reinhard Zumkeller_, Mar 06 2014