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

2, 3, 15, 105, 35, 231, 2145, 5005, 4641, 53295, 1616615, 119301, 21505, 7436429, 21489, 57998985, 3038795305, 4123, 13844919, 10393190665, 12838371, 299859855, 7292509103495, 12023917269, 70691995, 37198413949697, 62483343, 2769282065, 98755025688454681

Offset

2,1

Comments

Product of n-th row in triangle A171637;

All terms greater than 3 are odd, composite and squarefree numbers, cf. A024556.

n is prime iff n is a factor of a(n).

Product of the distinct primes in the Goldbach partitions of 2n. - Wesley Ivan Hurt, Sep 29 2020

Links

Reinhard Zumkeller, Table of n, a(n) for n = 2..2000

Formula

A020639(a(n)) = A020481(n); A006530(a(n)) = A020482(n);

A001221(a(n)) = A035026(n); A008472(a(n)) = A238778(n);

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;

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

Prog

(Haskell)
a238711 n = product $ filter ((== 1) . a010051') $
   map (2 * n -) $ takeWhile (<= 2 * n) a000040_list

Crossrefs

Cf. A000040, A010051, A238778, subsequence of A056911.

Sequence in context: A177012 A107413 A358119 * A362999 A165657 A091835

Adjacent sequences: A238708 A238709 A238710 * A238712 A238713 A238714

Keyword

nonn

Author

Reinhard Zumkeller, Mar 06 2014

Status

approved