1,1

This is to primorial (A002110) as anti-prime (A092680) is to prime (A000040). Max Alekseyev (maxale(AT)gmail.com) points out that every element 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.net/riesel.html http://www.prothsearch.net/riesel2.html there are no other such n up to 1200000. Therefore the next element of A066466 (if it exists) is greater than 3*2^1200000 ~= 10^361236. Hence the next element of the anti-primorials (if it exists) is greater than 679477248 *3*2^1200000 ~= 679477248 * 10^361236 ~= 6 * 10^361245.

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

a(1) = 3.

a(2) = 3 * 6 = 18.

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

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

Cf. A000040, A002110, A092680, A130874.

Sequence in context: A064846 A000853 A065402 this_sequence A069854 A057133 A001999

Adjacent sequences: A131486 A131487 A131488 this_sequence A131490 A131491 A131492

nonn

Jonathan Vos Post (jvospost2(AT)yahoo.com), Jul 28 2007