[seqfan] S and S complementary : cumulative sum is prime accordingly

[Eric Angelini]

Hello SeqFans,

  S = 1, 4, 6, 7, 11, 13, 14, 15, 18, 20, 21, 27, 28, 29, 30, 33, 34, ...
Scomp = 2, 3, 5, 8, 9, 10, 12, 16, 17, 19, 22, 23, 24, 25, 26, 31, 32, ...

All Natural numbers are shared between S and Scomp

Q is the cumulative sum of S (which is reproduced here, above Q):

  S = 1, 4, 6, 7, 11, 13, 14, 15, 18, 20, 21, 27, 28, 29, 30, 33, 34, ...
  Q = 1, 5,11,18, 29, 42, 56, 71, 89,109,130,157,185,214,244,277,311, ...

Non-primes in Q are marked "." and Primes are marked "p"; "n" is the rank
of the Primes in Q:

  Q = 1, 5,11,18, 29, 42, 56, 71, 89,109,130,157,185,214,244,277,311, ...
      .  p  p  .   p   .   .   p   p  p   .   p   .   .   .   p   p   
  n = .  2  3  .   5   .   .   8   9  10  .   12  .   .   .   16  17 

We see that Scomp is equal to the above "n" line (without the dots).

Pick thus any term of Scomp (e.g. "12"); this term says that the sum of
the first 12 terms of S is a Prime (here 157).

Pick any term of S (e.g. "13"), this term says that the sum of of the
first 13 terms of S is not a Prime (here 185).

If this is of interest, could someone check, compute and submit (in
september)? Thanks!
Best,
É.