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

Author

Reinhard Zumkeller, Sep 25 2014

Keywords

• nonn
• tabf

Comments

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

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

Examples

			.   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
		

Links

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

Crossrefs

Cf. A100678, A100695.

Programs

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