A131489 - OEIS

%I #10 Jun 03 2023 15:36:07

%S 3,18,1728,679477248

%N Anti-primorials, partial products of anti-primes A092680.

%C This is to primorial (A002110) as anti-prime (A092680) is to prime (A000040).

%C _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 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: http://www.prothsearch.com/riesel1.html http://www.prothsearch.com/riesel2.html 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]

%F a(n) = PRODUCT[k = 1..n] A092680(k).

%e a(1) = 3.

%e a(2) = 3 * 6 = 18.

%e a(3) = 3 * 6 * 96 = 1728.

%e a(4) = 3 * 6 * 96 * 393216 = 679477248.

%Y Cf. A000040, A002110, A092680, A130874.

%K nonn

%O 1,1

%A _Jonathan Vos Post_, Jul 28 2007