# [seqfan] Re: [LIKELY_SPAM] Re: 0-additive and first differences

Eric Angelini Eric.Angelini at kntv.be
Thu May 14 07:38:54 CEST 2015

```Thank you, Alois -- what I had in mind
I was unsure about all positive numbers occurring, sooner or later,
in the sequence itself or in the absolute
differences.
Is it obvious that 9, for instance, will
never show?

Best,
É.
Catapulté de mon aPhone

> Le 14 mai 2015 à 01:09, Heinz, Alois <alois.heinz at hs-heilbronn.de> a écrit :
>
>
> In a 0-additive sequence each term is the sum of two distinct
> *earlier* terms in exactly 0 ways.
>
> If you want the lexicographically first 0-additive sequence such
> that the terms in the sequence and their absolute first differences
> are all distinct you get:
>
> 1, 3, 7, 12, 18, 26, 9,  20, 34, 24, 39, 55, 22, 45, 66, 28, ...
> . 2, 4, 5, 6,  8,  17, 11, 14, 10, 15, 16, 33, 23, 21, 38, ...
>
> But then some positive numbers do not occur.
>
> Please note that 12 is the sum of 3 and 9 but 9 is not an
> earlier term.
>
> If you want the lexicographically first sequence such that the terms
> in the sequence and their absolute first differences are all distinct
> and each term is the sum of two distinct *other* terms in exactly 0 ways
> you get:
>
> 1, 3, 7, 12, 18, 26, 16, 31, 20, 37, 50, 22, 41, 64, 35, 56, 83, ...
> . 2, 4, 5, 6,  8,  10, 15, 11, 17, 13, 28, 19, 23, 29, 21, 27, ...
>
> But then again some positive numbers do not occur.
>
> Best regards, Alois
>
>> Am 13.05.2015 um 22:05 schrieb Frank Adams-Watters:
>> OK. 0-additive is different from what I thought.
>>
>> So, I want the lexicographically first sequence such that the sequence and its absolute first differences are all distinct. This starts as I stated, and it isn't in the database. A095115 is an approximation to this, but it doesn't really do any backtracking and is thus finite.
>>