A131489 Partial products of A092680.

3, 18, 1728, 679477248

Offset: 1

Author

Jonathan Vos Post, Jul 28 2007

Keywords

• nonn

Comments

Max Alekseyev points out that every term of A066466, except 4, must be of the form 3*2^k such that 3*2^(k+1)-1, 3*2^(k+1)+1 are twin primes. There are no such new k+1 (i.e., except known 1,2,6,18) below 1000. In other words, 3*2^n - 1, 3*2^n + 1 are twin primes for n=1,2,6,18. According to these tables in the Keller links there are no other such n up to 18*10^6. Therefore the next term of A066466 (if it exists) is greater than 3*2^(18*10^6) ~= 10^5418540. Hence the next element of the anti-primorials (if it exists) is greater than 679477248 * 10^5418540 > 10^5418548. [Updated by Max Alekseyev, May 23 2023]

Examples

			a(1) = 3.
a(2) = 3 * 6 = 18.
a(3) = 3 * 6 * 96 = 1728.
a(4) = 3 * 6 * 96 * 393216 = 679477248.
		

Links

• Ray Ballinger and Wilfrid Keller, List of primes k.2^n + 1 for k < 300
• Wilfrid Keller, List of primes k.2^n - 1 for k < 300

Crossrefs

Cf. A092680.

Formula

a(n) = Product_{k=1..n} A092680(k).