A285261 a(2n-1) and a(2n) represent the smallest fraction a(2n-1)/a(2n) needing n unit fractions.

1, 2, 2, 3, 4, 5, 8, 11, 16, 17, 77, 79, 732, 733, 27538, 27539

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