A129128 List of nodes generating two branches in the tree defined in sequence A129129.

2, 3, 5, 6, 7, 11, 10, 13, 17, 14, 19, 15, 18, 23, 29, 22, 21, 31, 26, 37, 41, 30, 43, 35, 34, 47, 33, 38, 53, 59, 42, 39, 61, 46, 67, 71, 50, 55, 73, 54, 79, 51, 58, 83, 65, 62, 57, 89, 66, 97, 101, 70, 103, 107, 74, 109, 69, 78, 85, 77, 82, 75, 113, 86, 127, 95, 90, 131, 137

Offset: 1

Author

Alford Arnold, Mar 31 2007

Keywords

• nonn
• tabf

Comments

The odd numbers begin 1 3 5 7 9 11 ... therefore a(n) begins 2 3 5 6 7 ...

Examples

			The tree begins
  1
  2
  3 4
  5 6 8
  7 10 9 12 16
  11 14 15 20 18 24 32
  ...
The array is a tree structure as described by A128628. If a node value has only one branch the value is twice that of its parent node. If it has two branches one is twice that of its parent node but the other is adjusted as indicated below:
(1) pick an odd number (e.g. 135)
(2) calculate its prime factorization (135 = 5*3*3*3)
(3) note the least prime factor (LPF(135) = 3)
(4) note the index of the LPF (index(3) = 2)
(5) subtract one from the index (2-1 = 1)
(6) calculate the prime associated with the value in step five (prime(1) = 2)
(7) The parent node generating the odd number 135 is (2/3)*135 = 90.
therefore 90 is a member of A129128.
		

Crossrefs

Cf. A020639, A129129.