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Search: id:A100140
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| A100140 |
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Largest denominator of greedy Egyptian fraction sum for M/N. |
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+0
1
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| 2, 6, 4, 20, 3, 231, 24, 45, 20, 4070, 12, 2145, 231, 120, 240, 3039345, 45, 2359420, 180, 1428, 4070, 1019084, 120, 53307975, 2145, 1350, 1428, 1003066152, 120, 1127619917796295, 16800, 26796, 3039345, 1104740, 72, 884004, 2359420, 1288092
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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Each term gives the largest of the N-1 terms in A050210 corresponding to the fractions with denominator N.
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REFERENCES
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Guy, R. K. "Egyptian Fractions." section D11 in "Unsolved Problems in Number Theory", 2nd ed. New York: Springer-Verlag, pp. 158-166, 1994.
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LINKS
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Robert Munafo, Largest Denominator of Greedy Egyptian Fraction Sum for M/N
Eric Weisstein's World of Mathematics, Egyptian Fractions.
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EXAMPLE
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Consider a(5). There are 4 fractions with 5 in the denominator: 1/5=1/5, 2/5=1/3+1/15, 3/5=1/2+1/10 and 4/5=1/2+1/4+1/20. Of these, the largest denominator is 20, so a(5)=20.
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PROGRAM
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/* MACSYMA or maxima */ egypt(x) := block([i, n, d, p, e, on, od], ( n : num(x), d : n/x, on : n, od : d, p : 0, e : [], for i:1 while x>0 do ( n : num(x), d : n/x, p : fix((d+n-1)/n), x : x - 1/p, e : append(e, [p]) ), return(p) ) ); for b:2 step 1 through 100 do ( max:2, for a:2 step 1 through b-1 do ( if gcd(a, b)=1 then ( m : egypt(a/b), if m>max then max : m ) ), print("a[", b, "]=", max) ), t$
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CROSSREFS
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Cf. A050210, A098853.
Sequence in context: A063427 A066092 A100695 this_sequence A009262 A127699 A124838
Adjacent sequences: A100137 A100138 A100139 this_sequence A100141 A100142 A100143
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KEYWORD
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nonn
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AUTHOR
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Robert P. Munafo (Robert.P.Munafo.86(AT)Alum.Dartmouth.ORG), Nov 06 2004
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