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Old 2010-12-01, 04:01   #1
sean
 
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Default Numbers wanted for OEIS sequences

The OEIS has a number of sequences needing more terms but which are currently blocked on finding factors of various numbers. In some cases, it would suffice to find a single factor, in other cases complete factorization is required. This list should not be considered exhaustive.

A046461 Is Smarandache(691) a semiprime.
A063684 Factorization of 105!+2.
A078781 Is 151!-1 a semiprime.
A080802 Is 151!-1 a semiprime.
A081715 Is 3^514+2 a semiprime.
A085745 Is 2^1239+1239 a semiprime.
A085747 Is 90!+97 a semiprime.
A099954 Is Fibonacci(1801) a semiprime.
A115101 Factorization of Lucas(2602).
A115973 Factorization of 101^101+1
A165767 Is 2^669-669 a semiprime.
A167937 Is 114!+1 a semiprime.
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Old 2010-12-01, 04:28   #2
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Quote:
Originally Posted by sean View Post
A078781 Is 151!-1 a semiprime.
A080802 Is 151!-1 a semiprime.
A factorization of 154!-1 would also be nice. Note that 157 / 37272934189201737869016720929 are also members.
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Old 2010-12-01, 06:39   #3
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Here's another one:

Euclid-Mullin-Sequence: A000945 and an overview here (needs first factor of a C256 of index 47).

Or the smallest open Sequence of Home Prime Base 10 for n=49 (Factorization of index 103 of C178).
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Old 2010-12-01, 13:35   #4
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Quote:
Originally Posted by sean View Post
The OEIS has a number of sequences needing more terms but which are currently blocked on finding factors of various numbers. In some cases, it would suffice to find a single factor, in other cases complete factorization is required. This list should not be considered exhaustive.

A046461 Is Smarandache(691) a semiprime.
A063684 Factorization of 105!+2.
A078781 Is 151!-1 a semiprime.
A080802 Is 151!-1 a semiprime.
A081715 Is 3^514+2 a semiprime.
A085745 Is 2^1239+1239 a semiprime.
A085747 Is 90!+97 a semiprime.
A099954 Is Fibonacci(1801) a semiprime.
A115101 Factorization of Lucas(2602).
A115973 Factorization of 101^101+1
A165767 Is 2^669-669 a semiprime.
A167937 Is 114!+1 a semiprime.
What is this "fetish" that people seem to have for semi-primes? ("p2's")???
Some of the numbers mentioned above are well within current capabilities.
Some are just out of reach (e.g. 2^1239 + 1239, 151!-1).
Some are well beyond them. (e.g. F1801, L2602)
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Old 2010-12-01, 14:17   #5
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Quote:
Originally Posted by R.D. Silverman View Post
What is this "fetish" that people seem to have for semi-primes? ("p2's")?
It's selection bias: detecting semiprimes requires factorization of a 'pure' composite, and this thread is looking for sequences requiring hard factorizations. Similarly, to be large enough to be difficult but also small enough to be doable, most of these sequences have exponential growth; that's also an artifact of our selection, since most OEIS sequences don't share that feature.
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Old 2010-12-10, 19:21   #6
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Also someone might consider submitting a b-file for sequences such as
http://oeis.org/A078604
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Old 2010-12-11, 17:03   #7
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Quote:
Originally Posted by sean View Post
The OEIS has a number of sequences needing more terms but which are currently blocked on finding factors of various numbers. In some cases, it would suffice to find a single factor, in other cases complete factorization is required. This list should not be considered exhaustive.

A046461 Is Smarandache(691) a semiprime.
A063684 Factorization of 105!+2.
A078781 Is 151!-1 a semiprime.
A080802 Is 151!-1 a semiprime.
A081715 Is 3^514+2 a semiprime.
A085745 Is 2^1239+1239 a semiprime.
A085747 Is 90!+97 a semiprime.
A099954 Is Fibonacci(1801) a semiprime.
A115101 Factorization of Lucas(2602).
A115973 Factorization of 101^101+1
A165767 Is 2^669-669 a semiprime.
A167937 Is 114!+1 a semiprime.
If CRG can help me with 1 or 2 things I may have a PARI code to search for numbers in A046461 , pretty much what I need is to count the factors to make sure it's only 2 and check to see only 1's in the exponents place. I solve that and I can come up with a script to test numbers.
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Old 2010-12-11, 17:24   #8
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Quote:
Originally Posted by science_man_88 View Post
If CRG can help me with 1 or 2 things I may have a PARI code to search for numbers in A046461 , pretty much what I need is to count the factors to make sure it's only 2 and check to see only 1's in the exponents place. I solve that and I can come up with a script to test numbers.
never mind:

Code:
if([isprime(factor(6)),1] && !isprime(6) ,print(factor(6)))
seems to work. now i replace 6 with eval(c) where c is a string from numbers 1 - x and i think it should work, put a for loop around it and change print(factor(6)) to print(x) and it should work fine for smaller ones.
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Old 2010-12-11, 17:26   #9
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Quote:
Originally Posted by science_man_88 View Post
never mind:

Code:
if([isprime(factor(6)),1] && !isprime(6) ,print(factor(6)))
seems to work. now i replace 6 with eval(c) where c is a string from numbers 1 - x and i think it should work, put a for loop around it and change print(factor(6)) to print(x) and it should work fine for smaller ones.
slight problem it doesn't just find the ones already in the sequence it finds a lot more because of a faulty check.
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Old 2010-12-11, 17:38   #10
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never mind the [] gives a fault anyways.

Code:
checking(y)= c="";for(z=1,y,c=concat(c,z));if(!isprime(eval(c)) ,print(y))
this is what I have now.

Last fiddled with by science_man_88 on 2010-12-11 at 18:07
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Old 2010-12-11, 18:33   #11
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http://oeis.org/A006881 has a small error in the PARI code ( a missing semicolon) I know this because i was thinking of going off this next, and then just using eval(c) in the place of n and checking if a integer sqrt was present I do that and we have a code for http://oeis.org/A046461 as well.
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