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Forum: sweety439 2022-01-16, 17:13
Replies: 0
Views: 6
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: 14
Views: 835
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: 14
Views: 835
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: 14
Views: 835
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: 279
Views: 28,971
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: 26
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: 26
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: 26
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: 14
Views: 835
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: 279
Views: 28,971
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: 10,626
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: 10,626
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: 279
Views: 28,971
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: 279
Views: 28,971
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: 279
Views: 28,971
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: 279
Views: 28,971
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: 279
Views: 28,971
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: 279
Views: 28,971
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...
Forum: sweety439 2022-01-12, 02:17
Replies: 279
Views: 28,971
Posted By sweety439
https://docs.google.com/spreadsheets/d/e/2PACX-1vT...

https://docs.google.com/spreadsheets/d/e/2PACX-1vTKkSNKGVQkUINlp1B3cXe90FWPwiegdA07EE7-U7sqXntKAEQrynoI1sbFvvKriieda3LfkqRwmKME/pubhtml

e.g.

for base b=311:

minimal prime (start with b+1)...
Forum: sweety439 2022-01-10, 23:24
Replies: 279
Views: 28,971
Posted By sweety439
done to 26

done to 26
Forum: sweety439 2022-01-10, 03:33
Replies: 279
Views: 28,971
Posted By sweety439
This is the prime game: Write down a prime...

This is the prime game:

Write down a prime number > 10, then you can always strike 0 or more digits to get a prime in this set: {11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73,...
Forum: sweety439 2022-01-10, 03:17
Replies: 279
Views: 28,971
Posted By sweety439
Proving the set of minimal primes (start with...

Proving the set of minimal primes (start with b+1) base b (let the set be S), is equivalent to:

* Proving all numbers in S are primes.
* Proving all proper subsequence of all elements in S which...
Forum: sweety439 2022-01-10, 02:27
Replies: 279
Views: 28,971
Posted By sweety439
I ran a program to compute the minimal primes...

I ran a program to compute the minimal primes (start with b+1) <= 2^32 in bases 17<=b<=36, now done to b=23
Forum: sweety439 2022-01-07, 00:38
Replies: 1,254
Views: 87,489
Posted By sweety439
S52 completed to n=5000 42,4822 52,0 ...

S52 completed to n=5000


42,4822
52,0
106,1175
113,0
158,0
216,1540
266,0
Forum: sweety439 2022-01-06, 20:10
Replies: 1,254
Views: 87,489
Posted By sweety439
R52 completed to n=5000 82,0 139,2564 ...

R52 completed to n=5000


82,0
139,2564
233,3180
239,1595
349,0
363,1396
372,0
Showing results 1 to 25 of 1000

 
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