Other interests

[kar_bon]

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 with statistics (out of date, updating needs too much FactorDB accesses)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)
- Euclid-Mullin Sequence up to index=51 (with C335)
- Generalized Fermat numbers
- 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 here)

[kar_bon]

I've included a page for Inverse Home Prime Base 8 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:
IHP₈(9737):i79 = P115 | IHP₈(1701):i65 = P114 | IHP₈(9865):i80 = P118
IHP₈(9759):i82 = P132 | IHP₈(1779):i77 = P119 | IHP₈(2895):i76 = P122
IHP₈(4615):i75 = P127 | IHP₈(1815):i95 = P151 | IHP₈(4895):i80 = P129
IHP₈(5731):i66 = P111 | IHP₈(9333):i71 = P113

K.Bonath

[kar_bon]

A new page for Home Prime Base 3 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 C150 at index 135 decomposed into P57*P93.

Please note: The given values for n=64 and 81 at MersenneWiki are out of date now.

Further efforts will be posted in here.

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

[kar_bon]

Home Prime Base 4 is online, too.

There're 14 startvalues <= 1000 without termination.

Further efforts are shown in this post.

[kar_bon]

Home Prime Base 5 is online.

There're 134 startvalues <= 1000 without termination.

Further efforts are shown in this post.

HP5(775):i88 = P134

[kar_bon]

Home Prime Base 6 is online.

There're 58 startvalues <= 10000 without termination.

Further efforts are shown in this post.

[kar_bon]

Home Prime Base 7 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]

Home Prime Base 8 is online.

There're 38 startvalues <= 1000 without termination.

Further efforts are shown in this post.

[Stargate38]

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]

Originally Posted by Stargate38

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.

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

Originally Posted by Stargate38

Same thing goes with multiples of 5 for bases 5, 10, 15, 20, etc.

Not correct, counterexamples:

HP5 (45) = P4 = 3313
IHP5 (45) = P12 = 681053105807

[Stargate38]

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