Problem 539

[Waldovski]

I'm a little confused about how P(1000)=510. If I understand the procedure correctly, this is how n=100 is supposed to go:

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100

2 6 10 14 18 22 26 30 34 38 42 46 50 54 58 62 66 70 74 78 82 86 90 94 98

6 14 22 30 38 46 54 62 70 78 86 94

6 22 38 54 70 86

22 54 86

22 86

86

According to the above procedure, P(100)=86 and P(1000)=342.

Did I misunderstand something? What am I doing wrong?

[mdean]

22 54 86

22 86

I think everything looked good until this step, which is clearly wrong. Either the left-most or right-most (or possibly both) number gets removed each step. That clearly didn't happen here.

[Waldovski]

I'm an idiot. Thank you and apologies.