cp's OEIS Frontend

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

%I A129128 #6 Sep 21 2024 02:26:35
%S A129128 2,3,5,6,7,11,10,13,17,14,19,15,18,23,29,22,21,31,26,37,41,30,43,35,
%T A129128 34,47,33,38,53,59,42,39,61,46,67,71,50,55,73,54,79,51,58,83,65,62,57,
%U A129128 89,66,97,101,70,103,107,74,109,69,78,85,77,82,75,113,86,127,95,90,131,137
%N A129128 List of nodes generating two branches in the tree defined in sequence A129129.
%C A129128 The odd numbers begin 1 3 5 7 9 11 ... therefore a(n) begins 2 3 5 6 7 ...
%e A129128 The tree begins
%e A129128   1
%e A129128   2
%e A129128   3 4
%e A129128   5 6 8
%e A129128   7 10 9 12 16
%e A129128   11 14 15 20 18 24 32
%e A129128   ...
%e A129128 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:
%e A129128 (1) pick an odd number (e.g. 135)
%e A129128 (2) calculate its prime factorization (135 = 5*3*3*3)
%e A129128 (3) note the least prime factor (LPF(135) = 3)
%e A129128 (4) note the index of the LPF (index(3) = 2)
%e A129128 (5) subtract one from the index (2-1 = 1)
%e A129128 (6) calculate the prime associated with the value in step five (prime(1) = 2)
%e A129128 (7) The parent node generating the odd number 135 is (2/3)*135 = 90.
%e A129128 therefore 90 is a member of A129128.
%Y A129128 Cf. A020639, A129129.
%K A129128 nonn,tabf
%O A129128 1,1
%A A129128 _Alford Arnold_, Mar 31 2007