seq. of primes related to Erdös' conjecture

[Maximilian Hasler]

>  did you have a look at that Benkoski & Erdös paper ?
>  (Math.Comp.28 (1974) 617-23)
>  They also mention an "old conjecture" for which Erdös offers $300 to settle it.
> I think the following is quite interesting and not in OEIS:
>  2,3,7,11,29,53,107,211,431,853,1709,3433,6857,13709,27427,54851
>  a(n)=least prime such that all subsets of { a(1),...,a(n) } have a different sum

I noticed that the variant "non-composite" instead of prime (i.e.
start with 1) leads to the sequence
1, 2, 5, 11, 23, 43, 89, 179, 359, 719, 1433, 2879, 5749, 11497, 22993, 45989
which seems identical to http://www.research.att.com/~njas/sequences/A064934
which however is defined as:
  Smallest prime (or non-composite) strictly greater than sum of
previous terms [with a(0)=1].

Is it easy to see that these 2 different definitions indeed give
identical sequences?
of course the second is much easier to compute !

Also note that for my initial sequence the property is not the same:
(2+3+7=13, but next term is 11, then sum=24 < a(5)=29;sum=53=a(6);
sum=106<a(7)=107; sum=213 > a(8)=211; sum=424<431, sum=855>853.
but from then on, it seems to have the same property.

Maximilian

PS: Even if the cited paper is called "On weird and pseudoperfect
numbers", I changed now the "subject" line, to avoid thread
stealing...