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A226623 Irregular array read by rows in which row n lists the smallest elements, in ascending order, of conjecturally all primitive cycles of positive integers under iteration by the Collatz-like 3x-k function, where k = A226630(n). 9
1, 5, 17, 19, 65, 73, 115, 2263, 2359, 2743, 2963, 3091, 3415, 3743, 4819, 113, 109, 95, 65, 989, 1153, 1165, 293, 511, 505, 625, 769, 211, 227, 251, 311, 1085, 2089, 7471, 10883, 13963, 15875, 16099, 1291, 1355, 1367, 1495, 1931, 2059, 2123, 2203, 2219, 2251 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The 3x-k function T_k is defined by T_k(x) = x/2 if x is even, (3x-k)/2 if x is odd, where k is odd.
Lagarias (1990) called a T_k cycle primitive if its elements are all relatively prime to k or, equivalently, if its elements are not a common multiple of the elements of another cycle.
LINKS
J. C. Lagarias, The set of rational cycles for the 3x+1 problem, Acta Arith. 56 (1990), 33-53.
EXAMPLE
The irregular array starts:
(k=1) 1, 5, 17;
(k=11) 19;
(k=17) 65, 73;
(k=19) 115;
a(4)=19 is the smallest number in the 3x-11 cycle {19,23,29,38}.
CROSSREFS
Row n begins with a(A226628(n)) and has length A226629(n).
The smallest starting value whose trajectory includes a(n) is A226627(n). The cycle associated with a(n) has length A226625(n) and A226626(n) odd elements of which A226624(n) is the largest
Sequence in context: A217079 A153320 A171253 * A171255 A304540 A306125
KEYWORD
nonn,tabf
AUTHOR
Geoffrey H. Morley, Jun 13 2013
STATUS
approved

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Last modified March 29 06:15 EDT 2024. Contains 371265 sequences. (Running on oeis4.)