A sequence S describing its partial sums

[Eric Angelini]

Hello SeqFans,
 
based on an equivalent idea and building rule as A121053,
here is a sequence I would appreciate someone to check,
define properly in good mathematical english, and submit
to the OEIS -- if of interest (I'll be back at my PC in
two weeks time -- and will do it myself if no one moves ;-)
 
a(n) says : "At position a(n) in S you will find the sum
of all terms from a(1) to a(n)"
 
S should be (computed by hand) :
 
1,3,4,8,6,22,9,16,53,11,133,13,279,15,573,69,18,1233,20,
2486,23,44,4995,25,10059,27,20145,29,40319,31,80669,33,
161371,35,322777,37,645591,39,12911221,41,25822483,43,
51645009,5039,103295057,47,...
 
S reads (from the beginning) :
- at position 1 there is the sum of all previously written terms [indeed, nil + 1=1]
- at position 3 there is the sum of all previously written terms [indeed, 1+ 3=4]
- at position 4 there is the sum of all previously written terms [indeed, 1+3+4=8]
- at position 8 there is the sum of all previously written terms [indeed, 1+3+4+8=16]
- at position 6 there is the sum of all previously written terms [indeed, 1+3+4+8+6=22]
- at position 22 there is the sum of all previously written terms [indeed, 1+3+4+8+6+22=44 and 44 is the 22nd term of S]
etc.
 
Best,
É.
(this seq. increases pretty fast sometimes -- then falls back to n+1...)
 
 
 
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