Prime tribonnaci numbers

[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.

[LaurV]

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...

[science_man_88]

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.

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

[CRGreathouse]

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.

[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.

[R.D. Silverman]

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.

[CRGreathouse]

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.