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A285261 a(2n-1) and a(2n) represent the smallest fraction a(2n-1)/a(2n) needing n unit fractions. 1
1, 2, 2, 3, 4, 5, 8, 11, 16, 17, 77, 79, 732, 733, 27538, 27539 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Huang Zhibin of China in April 2014 has verified that this fraction (27538/27539) needs 8 unit fractions.

LINKS

Table of n, a(n) for n=1..16.

Ron Knott, Egyptian Fractions

FORMULA

a(2n-1) = A097049(n); a(2n) = A097048(n). - Jon E. Schoenfield, Jan 11 2020

EXAMPLE

For n=1, 1/2 = 1/2;

for n=2, 2/3 = 1/3 + 1/3;

for n=3, 4/5 = 1/2 + 1/4 + 1/20 and 4/5 = 1/2 + 1/5 + 1/10;

for n=4, 8/11 = 1/2 + 1/6 + 1/22 + 1/66;

for n=5, 16/17 = 1/2 + 1/3 + 1/17 + 1/34 + 1/51;

for n=6, 77/79 = 1/2 + 1/3 + 1/8 + 1/79 + 1/474 + 1/632;

for n=7, 732/733 = 1/2 + 1/3 + 1/7 + 1/45 + 1/7330 + 1/20524 + 1/26388;

for n=8, 27538/27539 = 1/2 + 1/3 + 1/7 + 1/43 + 1/1933 + 1/14893663 + 1/1927145066572824 + 1/212829231672162931784; etc.

CROSSREFS

Cf. A097048, A097049.

Sequence in context: A116676 A240575 A176538 * A100483 A182613 A184259

Adjacent sequences:  A285258 A285259 A285260 * A285262 A285263 A285264

KEYWORD

hard,more,nonn

AUTHOR

Robert G. Wilson v, Apr 15 2017

STATUS

approved

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Last modified January 25 08:59 EST 2022. Contains 350565 sequences. (Running on oeis4.)