[seqfan] Re: More (composite) terms for A233281: 4181, 10877, 75077, ?

[Antti Karttunen]

On Tue, Feb 4, 2014 at 10:33 AM,  <seqfan-request at list.seqfan.eu> wrote:

> Message: 11
> Date: Mon, 3 Feb 2014 17:58:22 -0500
> From: Hans Havermann <gladhobo at teksavvy.com>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Subject: [seqfan] Re: More (composite) terms for A233281
> Message-ID: <AB7E92A4-83F8-45C8-A738-8236C60CC0A4 at teksavvy.com>
> Content-Type: text/plain; charset=us-ascii
>

> "Numbers n such that the least Fibonacci number F_k which is a multiple of n has a prime index, i.e. k is in A000040."
>
...
> Anyways, here are some additional values less than 10^8: 75077, 162133, 330929, 1256293, 1346269, 2662277, 3636121, 4226777, 9401893, 13455077, 14787181, 16485493, 21692189, 24157817, 24493061, 25532501, 29604893, 31432381, 39247393, 73780877, 75245777, 77337941.
>
> 75077 is the only additional composite < 10^5. In the remaining range, I don't know if there are other solutions.
>

Thank you Hans!

CC: Neil,

is here enough terms:
4181, 10877, 75077
to submit it as as sequence of its own? (with keyword:more )
"Composite numbers n such that A001177(n) is prime."
(A subset of http://oeis.org/A233281 )
Again, people are free to invent better names/definitions.


BTW, All are members of various Lucas / Frobenius pseudoprimes sequences:
https://oeis.org/search?q=4181+10877+75077&sort=&language=&go=Search


As what comes to the name of A233281, Hans objected its current version:

> "Numbers n such that the least Fibonacci number F_k which is a multiple of n has a prime index, i.e. k is in A000040."
>
> For those of us who think 'multiple' means more than one, 'positive multiple' (or an example) might have cleared this up.

Actually, I considered also these alternative names:

Numbers n such that the least p satisfying n|F_p (where F_p is p-th
Fibonacci number) is prime.

Numbers n such that the least p satisfying F_p = x*n (where F_p is
p-th Fibonacci number) is prime.

Numbers n such that the least k which satisfies {F_k = 0 mod n} is
prime, where F_k is k-th Fibonacci number.

Numbers n such that the least Fibonacci number F_k which satisfies
{F_k = 0 mod n} is Fibonacci number F_k with a prime index k.


Vote for the best or suggest a better one?


Yours,

Antti

>
> On Feb 1, 2014, at 9:08 PM, Antti Karttunen <antti.karttunen at gmail.com> wrote:
>
>>> http://oeis.org/A233281 that I recently submitted: "Numbers n such that A001177(n) is prime."
>>> So far, only two composites there, 4181 and 10877, are known.
>
>