A323725 a(n) is the last (and thus largest) denominator of an Egyptian fraction representing n, where each consecutive denominator is as small as possible.
1, 6, 57960, 36802906522516375115639735990520502954652700
Offset: 1
Keywords
Examples
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.)
Crossrefs
Programs
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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 def A323725(n): return egyptian_fraction((n,1))[-1] # Pontus von Brömssen, Aug 03 2020
Comments