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A323725
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a(n) is the last (and thus largest) denominator of an Egyptian fraction representing n, where each consecutive denominator is as small as possible.
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1
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OFFSET
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1,2
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COMMENTS
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Values grow extremely quickly, a(5) has 142548 decimal digits.
The denominators for n = 3 are given in A140335.
The denominators for n = 4 are given in A281873.
The number of terms in the representation of n is A306349(n).
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LINKS
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EXAMPLE
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a(3) = 57960 because (1/1) + (1/2) + (1/3) + (1/4) + (1/5) + (1/6) + (1/7) + (1/8) + (1/9) + (1/10) + (1/15) + (1/230) + (1/57960) = 3 and the final and greatest denominator is 57960. (Sequence A140335 has the full list of denominators.)
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PROG
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(PARI) a(n)={my(s=n, k=1); while(s>1/k, s-=1/k; k++); while(s!=0, k=ceil(1/s); s-=1/k); k} \\ Andrew Howroyd, Sep 01 2019
(Python)
from sympy import egyptian_fraction
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CROSSREFS
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A140335 and A281873 are the denominatorial sequences for 3 and 4, respectively.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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