mersenneforum.org Prime tribonnaci numbers
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 2014-09-11, 08:31 #1 fivemack (loop (#_fork))     Feb 2006 Cambridge, England 33×239 Posts Prime tribonnaci numbers Define the tribonnaci numbers as f(n)=f(n-1)+f(n-2)+f(n-3), with f(0)=f(-1)=f(-2)=1 (I think this is the usual way to do it, with the first non-1 at index 1) I have wasted a few dozen CPU hours to determine that indices 1 2 4 5 8 10 11 17 21 24 30 61 93 148 322 447 1967 2986 give prime value, and indices 6197 8091 23391 25425 34683 35074 44169 45622 give pseudoprime values. Would someone with OEIS access be willing to submit the sequence? (My interest in the tribonnaci numbers is that T(3n) can be written as a ternary cubic with small coefficients evaluated at [T(n-1),T(n),T(n+1)], which feels as if there might be productive analogies with SNFS; but my algebraic geometry is not sufficient to contemplate the Jacobian of a ternary cubic) PS gnome terminal in ubuntu-12.04 appears to take time proportional to the length of the longest line in the terminal to scroll, and freezes all other terminal windows while scrolling. If that line contains, for example, the decimal expansion of T(45622), this can get vexing. Last fiddled with by fivemack on 2014-09-11 at 08:32
 2014-09-11, 09:18 #2 LaurV Romulan Interpreter     "name field" Jun 2011 Thailand 35×41 Posts According with how the original spelt, it should be called tribonacci, not tribonnaci I think that your sequence can start in many different ways, and the one you selected is not the "most logical", considering that fibo starts with 0,1, it should be correct to start it either with 0,0,1 (or equivalent 0, 1, 2, if you shift it with one), or with 0,1,1. In all those cases the sequence is different, and has different properties. However, the way you start it has the merit that only generates odd numbers, which can be interesting from the primality point of view, we don't need to fuss about the even terms...
2014-09-11, 12:19   #3
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26×131 Posts

Quote:
 Originally Posted by LaurV According with how the original spelt, it should be called tribonacci, not tribonnaci
there's actually at least one result that comes up for each but:
http://oeis.org/search?q=tribonacci&...lish&go=Search

shows the most results.

0, 0, 1
1, 1, 1
0, 1, 0
1, 1, 0,

are starts from index 0 within the first few pages of results.

Quote:
 Originally Posted by fivemack 1 2 4 5 8 10 11 17 21 24 30 61 93 148 322 447 1967 2986
http://oeis.org/A157611 is a shifted version of this when the sequence starts at f(0)=f(1)=f(2) =1

Last fiddled with by science_man_88 on 2014-09-11 at 12:44

2014-09-11, 13:27   #4
CRGreathouse

Aug 2006

135338 Posts

Quote:
 Originally Posted by fivemack Define the tribonnaci numbers as f(n)=f(n-1)+f(n-2)+f(n-3), with f(0)=f(-1)=f(-2)=1 (I think this is the usual way to do it, with the first non-1 at index 1) I have wasted a few dozen CPU hours to determine that indices 1 2 4 5 8 10 11 17 21 24 30 61 93 148 322 447 1967 2986 give prime value, and indices 6197 8091 23391 25425 34683 35074 44169 45622 give pseudoprime values. Would someone with OEIS access be willing to submit the sequence?
This is essentially
https://oeis.org/A157611
which has two more terms, 83355 and 116402.

Edit: science_man beat me to it.

Last fiddled with by CRGreathouse on 2014-09-11 at 13:27

 2014-09-11, 16:32 #5 fivemack (loop (#_fork))     Feb 2006 Cambridge, England 193516 Posts Thanks. The CPU hours really were wasted - I'd googled the prime values and found OEIS 056816, but hadn't realised that the reference to A157611 in the formula gave a table of indices.
2014-09-11, 22:17   #6
R.D. Silverman

Nov 2003

11101001001002 Posts

Quote:
 Originally Posted by fivemack Define the tribonnaci numbers as f(n)=f(n-1)+f(n-2)+f(n-3), with f(0)=f(-1)=f(-2)=1 (I think this is the usual way to do it, with the first non-1 at index 1) I have wasted a few dozen CPU hours to determine that indices 1 2 4 5 8 10 11 17 21 24 30 61 93 148 322 447 1967 2986 give prime value, and indices 6197 8091 23391 25425 34683 35074 44169 45622 give pseudoprime values. Would someone with OEIS access be willing to submit the sequence? (My interest in the tribonnaci numbers is that T(3n) can be written as a ternary cubic with small coefficients evaluated at [T(n-1),T(n),T(n+1)], which feels as if there might be productive analogies with SNFS; but my algebraic geometry is not sufficient to contemplate the Jacobian of a ternary cubic) PS gnome terminal in ubuntu-12.04 appears to take time proportional to the length of the longest line in the terminal to scroll, and freezes all other terminal windows while scrolling. If that line contains, for example, the decimal expansion of T(45622), this can get vexing.
Sigh.

As I always say, a little time with google can save a lot of computing.

Look up Perrin Sequences and papers by Dan Shanks and Perrin in
Math.Comp.

2014-09-12, 13:17   #7
CRGreathouse

Aug 2006

3·1,993 Posts

Quote:
 Originally Posted by fivemack Thanks. The CPU hours really were wasted - I'd googled the prime values and found OEIS 056816, but hadn't realised that the reference to A157611 in the formula gave a table of indices.
Another possibility would be to send your sequence to the superseeker which (among other things) checks for shifted sequences.

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