A247765 Table of denominators in the Egyptian fraction representation of n/(n+1) by the greedy algorithm.

2, 2, 6, 2, 4, 2, 4, 20, 2, 3, 2, 3, 42, 2, 3, 24, 2, 3, 18, 2, 3, 15, 2, 3, 14, 231, 2, 3, 12, 2, 3, 12, 156, 2, 3, 11, 231, 2, 3, 10, 2, 3, 10, 240, 2, 3, 10, 128, 32640, 2, 3, 9, 2, 3, 9, 342, 2, 3, 9, 180, 2, 3, 9, 126, 2, 3, 9, 99, 2, 3, 9, 83, 34362

Offset

1,1

Comments

A100678(n) = length of n-th row;

T(n, A100678(n)) = A100695(n).

Links

Seiichi Manyama, Rows n = 1..1000 of triangle, flattened (Rows n = 1..100 from Reinhard Zumkeller)

Example

.   1:  2
.   2:  2, 6
.   3:  2, 4
.   4:  2, 4, 20
.   5:  2, 3
.   6:  2, 3, 42
.   7:  2, 3, 24
.   8:  2, 3, 18
.   9:  2, 3, 15
.  10:  2, 3, 14, 231
.  11:  2, 3, 12
.  12:  2, 3, 12, 156
.  13:  2, 3, 11, 231
.  14:  2, 3, 10
.  15:  2, 3, 10, 240
.  16:  2, 3, 10, 128, 32640
.  17:  2, 3,  9
.  18:  2, 3,  9, 342
.  19:  2, 3,  9, 180
.  20:  2, 3,  9, 126

Prog

(Haskell)
import Data.Ratio ((%), numerator, denominator)
a247765 n k = a247765_tabf !! (n-1) !! (k-1)
a247765_tabf = map a247765_row [1..]
a247765_row n = f (map recip [2..]) (n % (n + 1)) where
   f es x | numerator x == 1 = [denominator x]
          | otherwise        = g es
          where g (u:us) | u <= x    = (denominator u) : f us (x - u)
                         | otherwise =  g us

Crossrefs

Cf. A100678, A100695.

Sequence in context: A110141 A339489 A293443 * A129750 A278234 A349330

Adjacent sequences: A247762 A247763 A247764 * A247766 A247767 A247768

Keyword

nonn,tabf

Author

Reinhard Zumkeller, Sep 25 2014

Status

approved