By-products and other curiosities - Page 2

mart_r · 2009-07-28, 17:18

Quote:

Originally Posted by wblipp

Unfortunately, PFGW show (3^797161-1)/2 is composite

Meh.
You don't think the number will change its mind someday?

Oh well... here's the minimal set of square numbers up to 8.5*10^26:
1
4
9
25
36
576
676
7056
80656
665856
2027776
2802276
22282727076
77770707876
78807087076
7888885568656
8782782707776
72822772707876
555006880085056
782280288087076
827702888070276
888288787822276
2282820800707876
7880082008070276
80077778877070276
88778000807227876
782828878078078276
872727072820287876
2707700770820007076
7078287780880770276
7808287827720727876
8008002202002207876
27282772777702807876
70880800720008787876
72887222220777087876
80028077888770207876
80880700827207270276
87078270070088278276
88002002000028027076
2882278278888228807876
8770777780888228887076
77700027222828822007876
702087807788807888287876
788708087882007280808827876

including the number 0² gives
0
1
4
9
25
36
576
676
665856
7888885568656
888288787822276 (<--- will this be the last number in the list??)

mart_r · 2009-08-08, 15:30

Digital sum of the last m digits of x^n < digital sum of x (for x < 10^m):
For n even, this is always 10^m-1, but for odd n there are some irregularities:
n=3, m=1: {8}
n=3, m=2: {87}
n=3, m=3: {887}
n=3, m=4: {8887}
n=3, m=5: {99868}
n=3, m=6: {978887}
n=3, m=7: {7978887}
n=5, m=1: {1...9}
n=5, m=2: {81, 87}
n=5, m=3: {887, 994}
n=5, m=4: {9983, 9994}
n=5, m=5: {98994, 99594}
n=5, m=6: {989594}
n=5, m=7: {9899982}
n=7, m=1: {8}
n=7, m=2: {78, 97}
n=7, m=3: {978}
n=7, m=4: {9978}
n=7, m=5: {69978}
n=7, m=6: {869978}
n=7, m=7: {9799978}

mart_r · 2009-09-05, 11:57

I wonder if anyone has thought of this before:
With this formula, you get the time on your "life-clock":
$2*(sqrt{age}+1)$ in hours
For example, if you're 36 then you're at 2 P.M. in the day of your life.

A similar formula projecting a lifespan into one year will return August, 1st for this age:
$sqrt{age}+1$ in months, starting at Jan. 1st or, more precisely, $(sqrt{age}+1)/12*365.2(42)5$ in days, depending on whether you want to take an average Julian or Gregorian year into account. Note that you have to count 6 hours, or 5 h 49 m 12 s respectively, of Feb. 29th, if you want to be that precise.

retina · 2009-09-05, 12:09

Quote:

Originally Posted by mart_r

I wonder if anyone has thought of this before:
With this formula, you get the time on your "life-clock":
$2*(sqrt{age}+1)$ in hours
For example, if you're 36 then you're at 2 P.M. in the day of your life.

A similar formula projecting a lifespan into one year will return August, 1st for this age:
$sqrt{age}+1$ in months, starting at Jan. 1st or, more precisely, $(sqrt{age}+1)/12*365.2(42)5$ in days, depending on whether you want to take an average Julian or Gregorian year into account. Note that you have to count 6 hours, or 5 h 49 m 12 s respectively, of Feb. 29th, if you want to be that precise.

Not many people have lived to be 121, some people have lived longer.

mart_r · 2009-09-05, 14:34

Quote:

Originally Posted by retina

Not many people have lived to be 121, some people have lived longer.

Actually and officially, only one woman has surpassed this age yet.
But I pictured the end of the range at the beginning of a life, i.e. at the age of 144.

cheesehead · 2009-09-05, 21:06

Quote:

Originally Posted by mart_r

With this formula, you get the time on your "life-clock":
$2*(sqrt{age}+1)$ in hours

Quote:

Originally Posted by mart_r

But I pictured the end of the range at the beginning of a life, i.e. at the age of 144.

$2*(sqrt{144}+1) = 26$ ??

- - -

Oh, I see -- you're starting at 2 AM

$2*(sqrt{0}+1) = 2$

- - -

??

TimSorbet · 2009-09-05, 21:35

Quote:

Originally Posted by cheesehead

Oh, I see -- you're starting at 2 AM

$2*(sqrt{0}+1) = 2$

Actually, people are 0 years old (but almost always measured in days/weeks/months so as to have a >0 measure

) before they're 1 year old.
So it starts at 0 (12 midnight) o'clock
$2*(sqrt{0}+0) = 0$
And so someone living to 144 would live from midnight to 2 am the next day. (similarly, a 121 year old would be midnight to midnight)

mart_r · 2009-09-06, 11:07

Quote:

Originally Posted by Mini-Geek

So it starts at 0 (12 midnight) o'clock
$2*(sqrt{0}+0) = 0$
And so someone living to 144 would live from midnight to 2 am the next day. (similarly, a 121 year old would be midnight to midnight)

??
If 121 years is midnight --> midnight, then it would have to be $2*(sqrt{age}/11*12)$ ?

It's a symbolic measure, and it just fits better with the "+1" term in it.
It's rather useless from a completely mathematical point of view.

And yes, if you're 144 that would be 2 A.M. again.
If I would go further, I'd say every soul reincarnates after 144 years, and so noone can surpass this age. Hey, how 'bout a "square root of age plus one" cult?

retina · 2009-09-06, 11:23

Quote:

Originally Posted by cheesehead

Oh, I see -- you're starting at 2 AM

$2*(sqrt{0}+1) = 2$

Maybe it starts at -9 months?

$2*(sqrt{-9/12}+1) = 2 + sqrt{3}i$

davar55 · 2009-09-06, 13:26

We always did know pregnancy was COMPLEX.

TimSorbet · 2009-09-06, 20:34

Quote:

Originally Posted by davar55

We always did know pregnancy was COMPLEX.

2009-09-05, 11:57	#14
mart_r Dec 2008 you know...around... 2×5²×17 Posts	I wonder if anyone has thought of this before: With this formula, you get the time on your "life-clock": $2(sqrt{age}+1)$ in hours For example, if you're 36 then you're at 2 P.M. in the day of your life. A similar formula projecting a lifespan into one year will return August, 1st for this age: $sqrt{age}+1$ in months, starting at Jan. 1st or, more precisely, $(sqrt{age}+1)/12365.2(42)5$ in days, depending on whether you want to take an average Julian or Gregorian year into account. Note that you have to count 6 hours, or 5 h 49 m 12 s respectively, of Feb. 29th, if you want to be that precise. Last fiddled with by mart_r on 2009-09-05 at 11:57

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2009-08-08, 15:30	#13
mart_r Dec 2008 you know...around... 2·5²·17 Posts	Digital sum of the last m digits of x^n < digital sum of x (for x < 10^m): For n even, this is always 10^m-1, but for odd n there are some irregularities: n=3, m=1: {8} n=3, m=2: {87} n=3, m=3: {887} n=3, m=4: {8887} n=3, m=5: {99868} n=3, m=6: {978887} n=3, m=7: {7978887} n=5, m=1: {1...9} n=5, m=2: {81, 87} n=5, m=3: {887, 994} n=5, m=4: {9983, 9994} n=5, m=5: {98994, 99594} n=5, m=6: {989594} n=5, m=7: {9899982} n=7, m=1: {8} n=7, m=2: {78, 97} n=7, m=3: {978} n=7, m=4: {9978} n=7, m=5: {69978} n=7, m=6: {869978} n=7, m=7: {9799978}

2009-09-06, 13:26	#21
davar55 May 2004 New York City 5×7×11² Posts	We always did know pregnancy was COMPLEX.