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COMMENTS
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Conjecture: this is a rearrangement of natural numbers.
"Changing the seed produces different sequences, some of which merge into each other:
s2=2,1,3,6,4,8,12,9,5,10,15,25,20,24,16,32,48,30,18,36,27,13,7,53
s3=3,1,2,6,4,8,12,9,5,10,15,25,20,24,16,32,48,30,18,36,27,13,7,53
s4=4,1,5,2,3,15,6,9,45,10,20,8,16,12,13,169,26,7,53,106,265,159,18
s5=5,1,2,4,3,15,6,9,45,10,20,8,16,12,13,169,26,7,53,106,265,159,18
s6=6,1,7,2,4,5,25,10,3,9,8,16,12,18,14,20,32,24,27,81,36,15,75,30,40
s7=7,1,2,5,3,6,4,14,21,9,8,10,15,35,20,16,11,17,12,18,13,19,38,76,95
s8=8,1,3,2,7,21,6,4,13,5,10,16,12,9,39,26,14,28,32,64,20,17,51,24,18
s9=9,1,2,3,5,4,6,10,8,12,15,25,20,24,16,32,48,30,18,36,27,13,7,53,106
s10=10,1,11,2,3,9,4,5,15,6,22,8,12,18,7,19,38,95,57,114,24,16,31,17,32
s11=11,1,2,7,3,4,14,6,8,28,12,16,56,21,9,18,24,5,35,10,29,319,22,15,25,20,30
In every case one may ask if the result is a rearrangement of the natural numbers."
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