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Forum: Twin Prime Search 2021-08-08, 06:13
Replies: 4
Views: 1,056
Posted By sweety439
It can be easily proven that there are eight...

It can be easily proven that there are eight k-values which have A001221((k-1)*k*(k+1)) < 4:

2, 3, 4, 5, 7, 8, 9, 17
Forum: Twin Prime Search 2021-08-08, 06:11
Replies: 4
Views: 1,056
Posted By sweety439
The two numbers which must be prime powers...

The two numbers which must be prime powers simultaneously are:


k mod 12 the forms for the two numbers
0 2^r*3^s+-1
1 2^r*3^s+1 and (2^r*3^s+2)/2
2 (3^r-1)/2 and 3^r-2
3 ...
Forum: Twin Prime Search 2021-08-08, 06:03
Replies: 4
Views: 1,056
Posted By sweety439
k mod 12 such k-values 0 A027856...

k mod 12 such k-values
0 A027856 (https://oeis.org/A027856) except 6 and 18 (i.e. A027856 (https://oeis.org/A027856) except the numbers not divisible by 4)
1 A325255...
Forum: Twin Prime Search 2021-08-08, 05:59
Replies: 4
Views: 1,056
Posted By sweety439
If k == 2 mod 6, then: ---either--- *...

If k == 2 mod 6, then:

---either---

* k+1 is power of 3, k is of the form 2^r*p^s with p prime, k-1 is prime power, the r-value of k must be 1 or the k will have algebra factors and cannot be...
Forum: Twin Prime Search 2021-08-08, 05:35
Replies: 4
Views: 1,056
Posted By sweety439
A related conjecture about twin primes

Are there infinitely many triples of three consecutive numbers whose product has exactly four different prime factors, i.e. A001221 (https://oeis.org/A001221)((k-1)*k*(k+1)) = 4? Reference:...
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