A092680 -id:A092680 - cp's OEIS frontend

A131489 Partial products of A092680.

3, 18, 1728, 679477248

Offset: 1

Jonathan Vos Post, Jul 28 2007

nonn

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]

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

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

Cf. A092680.

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

A092679 Numbers k such that 3*2^k has only one anti-divisor.

Original entry on oeis.org

0, 1, 5, 17

Offset: 1

Lior Manor, Mar 03 2004

Next term should be greater than 3*10^6 (cf. A181490).

See A066272 for definition of anti-divisor.

Cf. A066466, A092680, A181490.

A092679 = [i for i,n in enumerate(map(lambda x:3*2**x,range(20))) if len([d for d in range(2,n,2) if n%d and not 2*n%d]+[d for d in range(3,n,2) if n%d and 2*n%d in [d-1,1]])==1] # Chai Wah Wu, Aug 09 2014

A092680(n) = 3*2^a(n).

a(n) = A181490(n) - 1. - Max Alekseyev, Feb 14 2025

cp's OEIS Frontend

A131489 Partial products of A092680.

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