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Forum: sweety439 2022-01-20, 22:18
Replies: 15
Views: 888
Posted By sweety439
The conjecture 2 in post #1...

The conjecture 2 in post #1 (https://mersenneforum.org/showpost.php?p=592782&postcount=1) (i.e. A347568 (https://oeis.org/A347568) is full with 8 terms: {1, 3, 4, 10, 14, 122, 422, 432}):

Zhi-Wei...
Forum: sweety439 2022-01-20, 10:26
Replies: 401
Views: 29,833
Posted By sweety439
https://sites.google.com/view/williams-primes ...

https://sites.google.com/view/williams-primes

https://sites.google.com/view/nexus-prime
Forum: Prime Wiki 2022-01-20, 10:21
Replies: 195
Sticky: Prime-Wiki
Views: 70,526
Posted By sweety439
Now I search the Williams primes...

Now I search the Williams primes (https://www.rieselprime.de/ziki/Williams_prime) (of all 8 kinds) to n=5000 (now done to base 45) and create a website (https://sites.google.com/view/williams-primes)...
Forum: sweety439 2022-01-18, 10:11
Replies: 1,256
Views: 87,876
Posted By sweety439
Sierpinski conjectures (k*b^n+1)/gcd(k-1,b+1):...

Sierpinski conjectures (k*b^n+1)/gcd(k-1,b+1): [b,k]

(GFN and half GFN not counted)

[2,21181]

b=2, k<=21180

[3,1187]
Forum: sweety439 2022-01-18, 10:01
Replies: 1,256
Views: 87,876
Posted By sweety439
Riesel conjectures (k*b^n-1)/gcd(k-1,b-1): [b,k] ...

Riesel conjectures (k*b^n-1)/gcd(k-1,b-1): [b,k]

[2,23669]

b=2, k<=23668

[3,1613]

b<=4, k<=1612
Forum: Aliquot Sequences 2022-01-18, 09:53
Replies: 1,027
Views: 124,727
Posted By sweety439
Is this a new record for the largest number in a...

Is this a new record for the largest number in a terminate aliquot sequence? (the largest number in this sequence is index 2789 (http://factordb.com/index.php?id=1100000001517282545))
Forum: sweety439 2022-01-17, 06:17
Replies: 280
Views: 29,362
Posted By sweety439
find the set of the minimal primes (start with...

find the set of the minimal primes (start with b+1) base b for various bases b (2<=b<=36) is the target of the project in this thread.

minimal prime (start with b+1) base b is always minimal prime...
Forum: sweety439 2022-01-16, 17:13
Replies: 0
Views: 17
Posted By sweety439
Off-topic

Like Cunningham table (https://homes.cerias.purdue.edu/~ssw/cun/index.html) to various bases, is there any interest to factor the numbers similar to Fibonacci numbers A000045...
Forum: sweety439 2022-01-16, 17:05
Replies: 15
Views: 888
Posted By sweety439
There are complement of A065377...

There are complement of A065377 (https://oeis.org/A065377) and A065397 (https://oeis.org/A065397) of the primes A000040 (https://oeis.org/A000040) in OEIS: A065376 (https://oeis.org/A065376) and...
Forum: sweety439 2022-01-16, 16:55
Replies: 15
Views: 888
Posted By sweety439
Compare with the numbers with only one way to...

Compare with the numbers with only one way to write as:

"twice a positive square number" + "odd prime or twice an odd prime"

or

"twice a positive triangular number" + "odd prime or twice an...
Forum: sweety439 2022-01-16, 11:48
Replies: 15
Views: 888
Posted By sweety439
Related research: perfect power...

Related research: perfect power (https://oeis.org/A001597) (0 and 1 are not counted as perfect power) + prime (the even prime 2 is allowed)

OEIS sequences for this: A119748...
Forum: sweety439 2022-01-15, 07:11
Replies: 280
Views: 29,362
Posted By sweety439
Conjecture: There is no base b such that the...

Conjecture: There is no base b such that the largest minimal prime (start with b+1) and the second-largest minimal prime (start with b+1) have the same number of digits in base b, note that in the...
Forum: sweety439 2022-01-15, 06:55
Replies: 2
Views: 31
Posted By sweety439
b-file (or a-file): (rows m = 1 to m = 12 of...

b-file (or a-file):

(rows m = 1 to m = 12 of the triangle (indices i = 1 to i = 78), flattened, row m = 1 has index i = 1, row m = 2 has index i = {2,3}, row m = 3 has index i = {4,5,6}, row m = 4...
Forum: sweety439 2022-01-15, 06:46
Replies: 2
Views: 31
Posted By sweety439
Problem: Prove or disprove such terms are 0: ...

Problem: Prove or disprove such terms are 0:

a(5,3): Are there any k such that sigma(k)/k = 5/3?
a(5,4): Are there any k such that sigma(k)/k = 5/4?
a(7,5): Are there any k such that sigma(k)/k...
Forum: sweety439 2022-01-15, 06:44
Replies: 2
Views: 31
Posted By sweety439
A new idea for OEIS "triangle read by rows" sequence

Triangle read by rows: a(m,n) = the gcd(m,n)-th number k such that sigma (https://oeis.org/A000203)(k)/k = m/n (i.e. the abundancy (https://mathworld.wolfram.com/Abundancy.html) of k is m/n, note...
Forum: sweety439 2022-01-14, 02:44
Replies: 15
Views: 888
Posted By sweety439
Now OEIS has sequences about these two...

Now OEIS has sequences about these two conjectures!!! A347567 (https://oeis.org/A347567) A347568 (https://oeis.org/A347568)
Forum: sweety439 2022-01-13, 11:42
Replies: 280
Views: 29,362
Posted By sweety439
all bases b<=36 are done. the original text...

all bases b<=36 are done.

the original text file for base 35 is too large (1743 KB) to upload, thus zipped it
Forum: Aliquot Sequences 2022-01-13, 08:04
Replies: 13
Views: 10,647
Posted By sweety439
No, see the graph in page 8 of...

No, see the graph in page 8 of https://arxiv.org/pdf/1610.07471.pdf, 137438691328 is also such number (untouchable perfect number, hermit number) like 28
Forum: Aliquot Sequences 2022-01-13, 08:01
Replies: 13
Views: 10,647
Posted By sweety439
I found that there are sequences about this in...

I found that there are sequences about this in OEIS:

A283152 (https://oeis.org/A283152) 2-untouchable numbers: {208, 250, 362, 396, 412, 428, 438, 452, 478, 486, 494, 508, 672, 712, 716, 772, 844,...
Forum: sweety439 2022-01-13, 06:36
Replies: 280
Views: 29,362
Posted By sweety439
but it is my newer researching result, and I...

but it is my newer researching result, and I think that it is important, sometimes I update my old posts, such as #208 (https://mersenneforum.org/showpost.php?p=593116&postcount=208) and #215...
Forum: sweety439 2022-01-13, 06:31
Replies: 280
Views: 29,362
Posted By sweety439
This is the smallest GFN primes and the smallest...

This is the smallest GFN primes and the smallest GRU primes in bases b<=64

Note 1: we do not include the case where the base of the GFNs is perfect odd power and the case where the base of the...
Forum: sweety439 2022-01-12, 13:28
Replies: 280
Views: 29,362
Posted By sweety439
When I have a new researching result about my...

When I have a new researching result about my project (i.e. finding and proving the set of minimal primes (start with b+1) in bases 2<=b<=36), I either post on this thread or update my article...
Forum: sweety439 2022-01-12, 04:57
Replies: 280
Views: 29,362
Posted By sweety439
look the size for the data files, my heuristic...

look the size for the data files, my heuristic argument (https://primes.utm.edu/glossary/xpage/Heuristic.html) is really true, i.e. the number of minimal primes (start with b+1) <= fixed limit (2^32...
Forum: sweety439 2022-01-12, 04:49
Replies: 280
Views: 29,362
Posted By sweety439
done to base b=31 the original text file for...

done to base b=31

the original text file for base 31 is too large (1546 KB) to upload, thus zipped it
Forum: sweety439 2022-01-12, 04:46
Replies: 280
Views: 29,362
Posted By sweety439
These are the data for "minimal primes (start...

These are the data for "minimal primes (start with b+1)" <= 2^32 in bases b=22 to b=26, they are in my project, see my article...
Showing results 1 to 25 of 1000

 
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