[seqfan] Sum of the a(n) first terms of S is not in S

[Eric Angelini]

Hello SeqFans,
The sum of the a(n) first terms of S is not in S :

S = 2,3,4,6,7,8,10,11,12,13,14,16,17,18,19,20,21,22,23,24,25,26,27,28,29,31,32,33,34,35,36,37,38,39,41,42,43,44,45,46,47,48,49,50,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,77,78,79,80,81,82,83,84,85,86,87,88,89,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,142,...

Example:
for n=1, a(n)=a(1)=2: the sum of the first 2 terms (2+3=5) is not in S;
for n=2, a(n)=a(2)=3: the sum of the first 3 terms (2+3+4=9) is not in S;
for n=3, a(n)=a(3)=4: the sum of the first 4 terms (2+3+4+6=15) is not in S;
for n=4, a(n)=a(4)=6: the sum of the first 6 terms (2+3+4+6+7+8=30) is not in S;
for n=5, a(n)=a(5)=7: the sum of the first 7 terms (2+3+4+6+7+8+10=40) is not in S;
...

Missing terms of S:
M = 1,5,9,15,30,40,51,76,90,106,123,141,180,201,223,246,270,295,...

Neither S nor M are in the OEIS.

Best,
É.