/sci/ - Science & Math » Thread #13880185

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A challenge for you

Anonymous Mon 22 Nov 19:05:20 2021 No.13880185 View Reply Original Report

Quoted By: >>13880242 >>13880319 >>13880383 >>13880406 >>13882208 >>13882233 >>13883138 >>13883320 >>13883598

>take any number
>add all of its prime factors together
>take that number and add all of its prime factors together
>repeat until you reach a prime
I defy any and all of you to beat the number 4677862, which takes a whopping 14 steps to reach a prime!

Anonymous

Anonymous Mon 22 Nov 2021 19:25:11 No.13880242 Report

Quoted By:

>>13880185
8675309

Anonymous

Anonymous Mon 22 Nov 2021 19:50:26 No.13880319 Report

Quoted By:

>>13880185
4

Wait, did I misunderstand the rules?

Anonymous

Anonymous Mon 22 Nov 2021 20:12:40 No.13880383 Report

Quoted By: >>13882120

>>13880185
Other than 4, I found that
14033577 takes 15 steps.
and 56134292 takes 16.

I checked only up to 1e8 though.

Anonymous

Anonymous Mon 22 Nov 2021 20:20:40 No.13880406 Report

Quoted By: >>13882442

>>13880185
>take any number
Pi

Anonymous

Anonymous Tue 23 Nov 2021 09:24:13 No.13882120 Report

Quoted By: >>13882165

>>13880383
How did you do that so quickly
That number took me all night to find

Anonymous

Anonymous Tue 23 Nov 2021 09:43:18 No.13882165 Report

Quoted By: >>13882451 >>13883049

>>13882120
Wait, did you search the numbers by hand?

Anonymous

Anonymous Tue 23 Nov 2021 10:02:15 No.13882208 Report

Quoted By:

>>13880185
1 doesn't have any prime factors therefore it beats any number.

Anonymous

Anonymous Tue 23 Nov 2021 10:08:54 No.13882233 Report

Quoted By: >>13882460

>>13880185
Algorithm to produce a number taking $n$ steps:
Take for example your number 4677862 and write it as a sum of 2's and 3's (you can always do that if the number is bigger than 3). So
$4677862 = 2 + \cdot + 2 =2338931 \cdot 2$ .
Now consider the product of these 2's and 3's. This product n a number which takes 1 step more than the previous.
So if we do that to a number taking $n$ steps you will produce a number taking $n+1$ steps.

Anonymous

Anonymous Tue 23 Nov 2021 12:01:35 No.13882442 Report

Quoted By: >>13882501

>>13880406
pi is not a number

Anonymous

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Anonymous Tue 23 Nov 2021 12:05:00 No.13882451 Report

Quoted By:

>>13882165
obviously not

Anonymous

Anonymous Tue 23 Nov 2021 12:09:02 No.13882460 Report

Quoted By:

>>13882233
That doesn't give a great solution though. You obviously want as small a number as possible which takes $n$ steps.
$2^{2338931}$ does not look good

Anonymous

Anonymous Tue 23 Nov 2021 12:35:37 No.13882501 Report

Quoted By:

>>13882442
True. It is the first letter in ??????????.
It is actually frequently used as the name of a number.

Anonymous

Anonymous Tue 23 Nov 2021 16:55:57 No.13883049 Report

Quoted By:

>>13882165
With a calculator

Anonymous

Anonymous Tue 23 Nov 2021 17:01:50 No.13883066 Report

Quoted By:

Anonymous

Anonymous Tue 23 Nov 2021 17:15:32 No.13883096 Report

Quoted By:

2
Done

Anonymous

Anonymous Tue 23 Nov 2021 17:36:49 No.13883138 Report

Quoted By: >>13883304

>>13880185
Let's see if I can build one...
7 -> (2+5), 2*5=10
10 -> (3+7), 3*7=21
21 -> (19+2), 19*2=38
38 -> (31+7), 31*7=217
217 -> (199+13+3), 199*13*3=13179
13179 -> (13177+2), 13177*2=26354
...
I can keep going. I'm just taking the previous number, subtracting prime numbers from it until it's 0 (without repeat numbers). Then taking those primes and multiplying them to get the next number.

Anonymous

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Anonymous Tue 23 Nov 2021 18:28:04 No.13883304 Report

Quoted By:

>>13883138
Impressive... Although 26354 (6 steps to reach a prime) gets beaten by the much smaller 393 (7 steps)

Anonymous

Anonymous Tue 23 Nov 2021 18:30:42 No.13883320 Report

Quoted By:

>>13880185
>4677862
From what number did you start?

Anonymous

Anonymous Tue 23 Nov 2021 19:00:40 No.13883459 Report

Quoted By: >>13885238

A047830 as a simple table
n a(n)
0 2
1 4
2 14
3 26
4 62
5 134
6 393
7 1774
8 13682
9 41037
10 167073
11 334142
12 4677862
13 14033577
14 79464886
15 476789307
16 3488435822
17 34884358195

Anonymous

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Anonymous Tue 23 Nov 2021 19:32:34 No.13883598 Report

Quoted By: >>13885238

>>13880185
Stop playing around with a calculator and learn number theory

Anonymous

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Anonymous Wed 24 Nov 2021 05:25:04 No.13885238 Report

Quoted By:

>>13883459
Sir, I don't see any number which takes more than 15 steps
>>13883598
How?

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