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kar_bon 2010-06-03 21:01

Other interests
 
Here you can post stuff regarding to other interests I display on my pages.

So far there're information of

- Aliquot sequences for n<1000000: all open seqs. with statistics (out of date, updating needs too much FactorDB accesses)
- Home Prime Base 2: 7 open seqs. for n<10000 (listed up to n=12000)
- Home Prime Base 3: 31 open seqs. for n<1000 (current status see post#3)
- Home Prime Base 4: 17 open seqs. for n<1000 (current status see post#4)
- Home Prime Base 5: 134 open seqs. for n<=1000 (current status see post#5)
- Home Prime Base 6: 58 open seqs. for n<10000 (current status see post#6)
- Home Prime Base 7: 186 open seqs. for n<1000 (current status see post#7)
- Home Prime Base 8: 38 open seqs. for n<1000 (current status see post#8)
- Home Prime Base 10: 537 open seqs. for n<10000 (listed up to n=11500 plus special forms like powers of 2/3/10, ...)
- Inverse Home Prime Base 8: for n<10000 (current status see post#2)
- [url=http://oeis.org/A000945]Euclid-Mullin Sequence[/url] up to index=51 (with C335)
- [url=http://www1.uni-hamburg.de/RRZ/W.Keller/GFNsmall.html]Generalized Fermat numbers[/url]
- Primes of the form k*b^b+1, k<=10000, b<=1000
- Primes of the form k*b^b-1, k<=10000, b<=1000
- Factorizations of Smarandache-type numbers
- Smallest primes/semiprimes for 10^n up to n=150
- CRUS condensed table (a daily update can be found [url=http://www.noprimeleftbehind.net/crus/tab/CRUS_tab.htm]here[/url])

kar_bon 2012-04-23 23:35

Inverse Home Prime Base 8
 
I've included a page for [url=http://www.rieselprime.de/Others/InverseHomePrime8.htm]Inverse Home Prime Base 8[/url] with all open sequences for n<=10000 (terminations with 70+ digits are given).

So far 170 sequences are not terminated.

New terminations found since then:
IHP[sub]8[/sub](9737):i79 = P115 | IHP[sub]8[/sub](1701):i65 = P114 | IHP[sub]8[/sub](9865):i80 = P118
IHP[sub]8[/sub](9759):i82 = P132 | IHP[sub]8[/sub](1779):i77 = P119 | IHP[sub]8[/sub](2895):i76 = P122
IHP[sub]8[/sub](4615):i75 = P127 | IHP[sub]8[/sub](1815):i95 = P151 | IHP[sub]8[/sub](4895):i80 = P129
IHP[sub]8[/sub](5731):i66 = P111 | IHP[sub]8[/sub](9333):i71 = P113

K.Bonath

kar_bon 2012-06-30 07:01

Home Prime Base 3
 
A new page for [url=http://www.rieselprime.de/Others/HomePrime3.htm]Home Prime Base 3[/url] is online now.

So far 31 startvalues <= 1000 are without termination. All terminations with >=70 digits are given.

I've also extended the seq. for n=64: A [url=http://factordb.com/sequences.php?se=3&aq=64&action=range&fr=135&to=135]C150 at index 135[/url] decomposed into P57*P93.

Please note: The given values for n=64 and 81 at [url=http://www.mersennewiki.org/index.php/Base_3_Home_Prime_Results]MersenneWiki[/url] are out of date now.

Further efforts will be posted in here.

New terminations found since then:
HP3(581):i118 = P128

kar_bon 2012-07-03 16:38

Home Prime Base 4
 
[url=http://www.rieselprime.de/Others/HomePrime4.htm]Home Prime Base 4[/url] is online, too.

There're 14 startvalues <= 1000 without termination.

Further efforts are shown in this post.

kar_bon 2012-07-03 16:38

Home Prime Base 5
 
[url=http://www.rieselprime.de/Others/HomePrime5.htm]Home Prime Base 5[/url] is online.

There're 134 startvalues <= 1000 without termination.

Further efforts are shown in this post.

HP5(775):i88 = P134

kar_bon 2012-07-03 16:38

Home Prime Base 6
 
[url=http://www.rieselprime.de/Others/HomePrime6.htm]Home Prime Base 6[/url] is online.

There're 58 startvalues <= 10000 without termination.

Further efforts are shown in this post.

kar_bon 2012-07-03 16:38

Home Prime Base 7
 
[url=http://www.rieselprime.de/Others/HomePrime7.htm]Home Prime Base 7[/url] is online.

There're 186 startvalues <= 1000 without termination.

Further efforts are shown in this post.

HP7(933):i65 = P139
HP7(542):i58 = P125

kar_bon 2012-07-03 16:38

Home Prime Base 8
 
[url=http://www.rieselprime.de/Others/HomePrime8.htm]Home Prime Base 8[/url] is online.

There're 38 startvalues <= 1000 without termination.

Further efforts are shown in this post.

Stargate38 2012-07-06 13:15

For Inverse Home Primes (bases 2, 4, 6, 8, etc.), the starting number can't be even because the whole sequence would be divisible by 2 and therefore composite. Same thing goes with multiples of 5 for bases 5, 10, 15, 20, etc.

kar_bon 2012-07-06 19:03

[QUOTE=Stargate38;304171]For Inverse Home Primes (bases 2, 4, 6, 8, etc.), the starting number can't be even because the whole sequence would be divisible by 2 and therefore composite.[/quote]

I know that: see the headline of the page for IHP8.


[QUOTE=Stargate38;304171]Same thing goes with multiples of 5 for bases 5, 10, 15, 20, etc.[/QUOTE]

Not correct, counterexamples:

[url=http://factordb.com/sequences.php?se=5&aq=45&action=all]HP5 (45)[/url] = P4 = 3313
[url=http://factordb.com/sequences.php?se=15&aq=45&action=all]IHP5 (45)[/url] = P12 = 681053105807

Stargate38 2012-07-08 00:58

Oh. I didn't go deep enough. I'm doing IHP5(55) because it wasn't in the DB.


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