非線形数列

un+1=un^2-un+1, u1=2 (Euclid numbers)

x=2,3,7,43,1807,3263443,,, un~θ^a, θ~1.598, a=2^n

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1/2+1/3+1/7+1/43+1/1807+1/3263443+…=1

1/2+1/2=1

1/2+1/3+1/6=1

1/2+1/3+1/7+1/42=1

1/2+1/3+1/7+1/43+1/1806=1 (Egyptian fraction)

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1/x1+1/x2+…+1/xk=1 (x11/u1+1/u2+…+1/(uk-1)=1, 1/(uk-1)=1/uk+1/uk+1+1/uk+2+…

k=4

1/2+1/3+1/7+1/42=1 (max x4=u4-1)

1/2+1/4+1/6+1/12=1 (min x4)

k=5

1/2+1/3+1/7+1/43+1/1806=1 (max x5=u5-1)

1/2+1/4+1/10+1/12+1/15=1 (min x5)

1/2+1/4+1/7+1/14+1/28=1 (perfect number)

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