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A352543
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Numbers that end in a loop of size > 2 under iterations of A352544 (= half or add largest anagram).
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3
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549, 639, 801, 1035, 1098, 1278, 1503, 1602, 1611, 2025, 2070, 2196, 2511, 2556, 3006, 3123, 3159, 3204, 3222, 3411, 3861, 4050, 4140, 4149, 4383, 4392, 4635, 5022, 5112, 5589, 5679, 5913, 6012, 6165, 6246, 6318, 6345, 6408, 6444, 6795, 6813, 6822, 7047, 7245, 7713, 7722, 7785, 8100, 8280, 8298, 8757, 8766, 8784, 9203, 9270, 9459
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OFFSET
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1,1
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COMMENTS
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Most small starting values end in a cycle or loop of length 2 under iterations of A352544 (like 1 -> 2 -> 1, 3 -> 6 -> 3, or 49 -> 143 -> ... -> 7915 -> 17666 -> 8833 -> 17666, and some (listed in A352540) have an unbounded orbit like 89 (cf. A352542).
This sequence lists all other starting values, i.e., those which have a bounded orbit but don't end in a cycle of length 2. (A352544 obviously has no fixed points.)
All terms below a(54) = 9203 lead to the same loop 1611 -> 7722 -> 3861 -> 12492 -> 6246 -> 3123 -> 6444 -> 3222 -> 1611 of size 8.
The starting value 9203 is the only one below 10^4 leading to a different loop, of size 22: cf. EXAMPLE.
Sequence A352545 lists the representatives (smallest elements) of the distinct cycles of length > 2.
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LINKS
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EXAMPLE
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The number a(1) = 549 is the smallest starting value which leads into a cycle of length > 2 under iterations of the map A352544: namely, 549 -> 1503 -> 6813 -> 15444 -> 7722 which is element of the cycle [3861, 12492, 6246, 3123, 6444, 3222, 1611, 7722] of length 8, with representative = smallest member A352545(1) = 1611.
The starting value a(54) = 9203 is the only one below 10^4 leading to a different loop: it goes at once to 18523 -> 103844 -> 51922 -> 25961 -> 122482 -> 61241 -> 125452 -> 62726 -> 31363 -> 94694 -> 47347 -> 124790 -> 62395 -> 158927 -> 1146448 -> 573224 -> 286612 -> 143306 -> 71653 -> 148184 -> 74092 -> 37046 -> 18523, a loop of size 22, with representative = smallest member A352545(2) = 18523.
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PROG
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(PARI) is_A352543(n, L=99, a=[n])={for(i=1, L, a=concat(a, n=A352544(n)); #Set(a)>i||break); #a < L && #Set(a[-3..-1]) > 2}
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CROSSREFS
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Cf. A352544 (the iterated map) and further references there: A352540 (starting values not ending in a loop), A352541 (number of iterations to reach a value for the second time), A352545 (representatives of cycles of length > 2).
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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