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A130738 Greedy odd Egyptian fraction representation of 1 (without repeats). 0
3, 5, 7, 9, 11, 13, 23, 721, 979007, 661211444787, 622321538786143185105739, 511768271877666618502328764212401495966764795565, 209525411280522638000804396401925664136495425904830384693383280180439963265695525939102230139815 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) is the largest odd Egyptian fraction as yet unused, such that the sum of the Egyptian fractions so far does not exceed 1. The sum of a(n) is a greedy representation (greedy because each step bites off as much as possible) of 1, using only odd Egyptian fractions, all distinct.

Terms a(11)-a(13) were found by David Eppstein (see posting from Nov 09 1996), who says that he found them by applying EgyptOddGreedy[2/3,5] from his Egyptian fractions notebook.

REFERENCES

Mohammad K. Azarian, Sylvester's Sequence and the Infinite Egyptian Fraction Decomposition of 1, Problem 958, College Mathematics Journal, Vol. 42, No. 4, September 2011, p. 330. Solution published in Vol. 43, No. 4, September 2012, pp. 340-342

R. K. Guy, Unsolved Problems Number Theory, Sect D11.

LINKS

Table of n, a(n) for n=1..13.

David Eppstein, Egyptian fractions

David Eppstein, Egyptian fractions, Discussion, Nov 09 1996.

Index entries for sequences related to Egyptian fractions

EXAMPLE

E.g. a(8)=721 because 1/721 is the largest odd Egyptian fraction less than 1-1/a(1)-1/a(2)-1/a(3)-1/a(4)-1/a(5)-1/a(6)-1/a(7).

1/3 + 1/5 + 1/7 + 1/9 + 1/11 + 1/13 + 1/23 + 1/721 + 1/979007 + 1/661211444787 + 1/622321538786143185105739 + 1/511768271877666618502328764212401495966764795565 + 1/209525411280522638000804396401925664136495425904830384693383280180439963265695525939102230139815 = 1.

CROSSREFS

Cf. A002966, A169820.

Sequence in context: A143448 A226484 A261213 * A239036 A024323 A118820

Adjacent sequences: A130735 A130736 A130737 * A130739 A130740 A130741

KEYWORD

nonn,fini,full

AUTHOR

Jon Wild, Jul 06 2007

EXTENSIONS

Edited and a(11)-a(13) added by N. J. A. Sloane, May 29 2010, at the suggestion of Jan Szejko.

STATUS

approved

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Last modified December 7 04:29 EST 2022. Contains 358649 sequences. (Running on oeis4.)