[seqfan] Re: Help defining a sequence

[Allan Wechsler]

I prefer Ali Sada's version to Frank Adams-watters's, because the latter
consumes even elements inexorably, while the former at least occasionally
introduces new even elements.

On Fri, Dec 6, 2019 at 10:30 PM Frank Adams-watters via SeqFan <
seqfan at list.seqfan.eu> wrote:

> A simple variant of this is to add only one copy of the smallest even and
> the smallest odd element.
>
> Thus for n = 4, from the multiset {3,3,4}, we add 3+4 = 7. This gives us
> {3,7}, and a(4) = 7.
>
> Franklin T. Adams-Watters
>
>
> -----Original Message-----
> From: Ali Sada via SeqFan <seqfan at list.seqfan.eu>
> To: Sequence Fanatics Discussion List <seqfan at list.seqfan.eu>
> Cc: Ali Sada <pemd70 at yahoo.com>
> Sent: Wed, Dec 4, 2019 1:31 am
> Subject: [seqfan] Help defining a sequence
>
> Hi Everyone,
>
> I need some help defining the sequence below. I put several examples in
> order to make sure my language is clear.
>
> To find each term of the sequence, we take the numbers from 1 to n and put
> them in a set. We keep adding the least odd element (or elements) to the
> least even element (or elements) until we run out of options.
> a(n) is the largest number that results from the operations.
> We start with {1}. We have only one element, so a(1)=1
>
> Then we take the set {1,2}.  The smallest odd element is 1 and the
> smallest even element is 2. We add them and we get a(2)=3
>
> We take the set {1,2,3}. We add 1+2 = 3. Now, we have the multiset {3,3}.
> We don’t have any even element left, so a(3)=3 (the largest number
> resulted).
>
> We take the set {1,2,3,4}. We add 1 to 2 we get 3. Now we have the
> multiset {3,3,4}. Since we have two least odd elements, we add them both to
> the even element (4) and we get a(4)=10.
>
> Now we take the set {1,2,3,4,5}. We add 1 and 2 and we get the multiset
> {3,3,4,5}. We add the two 3’s to 4 and we get 10. Now we have the set
> {10,5}. It still has an odd element and an even element, so we continue.
> 10+5=15. a(5)=15.
>
> For the set {1,2,3,4,5,6}, the steps will be the same as before until we
> reach the set {10,5,6}. We add the least odd element (5) to the least even
> element (6) and we get the set {10,11}. We still have an odd element and an
> even element, so we add them. a(6)=10+11=21.
>
> For the set {1,2,3,4,5,6,7} we have the same steps as before until we get
> the set {10,5,6,7}. The least odd element in this set is 5, and the least
> even element is 6. We add them and we get 11. The new resulted set is
> {10,11,7}. Now, we add the least odd element (7) to the least even element
> (10) and we get 17. The resulted set is {11,17}. We ran out of even
> elements, and the largest number we got was 17. So, a(7)=17.
>
> Writing a program to find the terms of this sequence in VBA/Excel was
> difficult. I would really appreciate it if you could help me find the
> necessary terms for an OEIS sequence.
>
> The terms I found so far (and I might have made a mistake somewhere) are:
>
> 1, 3, 3, 10, 15, 21, 17, 21, 19, 29, 29, 49, 47, 49, 91, 75, 73, 75, 73,
> 75, 67, 83, 73, 75, 81, 75, 123, 121
>
> Best,
>
> Ali
>
>
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>