A129128 - OEIS

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

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OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..69.

EXAMPLE

The tree begins

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.

Sequence in context: A220355 A353954 A059041 * A355647 A367585 A164922

Adjacent sequences: A129125 A129126 A129127 * A129129 A129130 A129131

KEYWORD

nonn,tabf

AUTHOR

Alford Arnold, Mar 31 2007

STATUS

approved