[seqfan] Re: Smallest index of Fibonacci-like sequence containing n

Bob Selcoe rselcoe at entouchonline.net
Wed Nov 5 21:28:18 CET 2014


Appears that the same process using only positive numbers isn't in OEIS 
either: (1),2,2,3,2,4,3,2,4,4,3,5...

Cheers,
Bob Selcoe


--------------------------------------------------
From: "Frank Adams-Watters" <franktaw at netscape.net>
Sent: Wednesday, November 05, 2014 1:55 PM
To: <seqfan at list.seqfan.eu>
Subject: [seqfan] Re: Smallest index of Fibonacci-like sequence containing n

> This sequence is probably not present, but a number of related sequences 
> are. A035506 is a place to start looking.
>
> Franklin T. Adams-Watters
>
> -----Original Message-----
> From: Allan Wechsler <acwacw at gmail.com>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Wed, Nov 5, 2014 1:33 pm
> Subject: [seqfan] Smallest index of Fibonacci-like sequence containing n
>
>
> Any two non-negative integers can seed a Fibonacci-like sequence, F[0] = 
> A,
> F[1] = B, F[i+2] = F[i+1] + F[i].
>
> Let A+B be called the "index" of this sequence.
>
> Of all Fibonacci-like sequences containing, say, 18, the one with the
> smallest index is {2,1,3,4,7,11,18...}, with an index of 3. So I say A[18]
> = 3.
>
> If n is a classic Fibonacci number, A[n] = 1. If n is a Lucas number (like
> 18), then A[n] = 3. If n is twice a Fibonacci number (like 16) then A[n] =
> 2.
>
> I have calculated A[n] by hand for n from 1 to 24. It is quite possible
> that I have made mistakes, but the sequence I get is:
>
> {1,1,1,2,1,2,3,1,3,2,3,4,1,4,3,2,5,3,5,4,1,6,4,3, ...}
>
> This is not in OEIS. I would've submitted it, but I would like somebody
> else to check my arithmetic first, because it seems unlikely that such a
> simple concept wouldn't have been entered already. If nobody steps up to
> the place quickly I will cobble together some code and submit anyway.
> Thanks for your assistance, seqfans!
>
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