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%I #19 May 12 2023 09:10:10
%S 1,3,0,2,0,1,0,0,0,0,0,9,0,7,10,0,9,4,0,3,8,8,8,7,15,5,5,3,12,1,11,16,
%T 0,7,0,5,8,0,7,2,0,6,6,6,6,5,13,3,3,1,10,6,9,14,0,5,0,3,6,0,5,4,0,4,4,
%U 4,4,3,11,1,1,13,8,4,7,12,0,3,0,1,4,2,3,2,0,2,2,2,2,1,9,12,0
%N Define sequence S_n by: initial term = n, reverse digits and add 2 to get next term. It is conjectured that S_n always reaches a cycle. Sequence gives number of steps for S_n to reach a cycle.
%C Initial cycles have length 81 or 90.
%C There is one cycle of length 81 (least component is 3, all components have at most three digits, cf. A117521), 22 cycles of length 90 with 4-digit components (least components are 1013 + 2*k for k = 0, ..., 21, cf. A120214) and one cycle of length 45 with 4-digit components (least component is 1057, cf. A120215). Furthermore there are 22 cycles of length 1890 (least components are 100013 + 2*k for k = 0, ..., 21, cf. A120216), one cycle of length 945 (least component is 100057, cf. A120217) and 225 cycles of length 900 (least components are 100103 + 2*k for k = 0, ..., 224, cf. A120218), all having 6-digit components. It is conjectured that there are also cycles of increasing length with 8-, 10-, 12-, ... digit components. - _Klaus Brockhaus_, Jun 10 2006
%C From _Michael S. Branicky_, May 11 2023: (Start)
%C There are 22 cycles of length 19890 (least components are 10000013 + 2*k for k = 0, ..., 21), one cycle of length 9945 (least component 10000057), 225 cycles of length 18900 (least components are 10000103 + 2*k for k = 0, ..., 224) and 2250 cycles of length 9000 (least components are 10001003 + 2*k for k = 0, ..., 2249), all having 8-digit components.
%C These patterns continue. Specifically, there is one cycle of length 10^(n/2) - 55 (least component 10^(n-1) + 57), and there are 22 cycles of length 2*(10^(n/2) - 55) (least components 10^(n-1) + 13 + 2*k for k = 0, ..., 21), each for n = 4, 6, 8, 10, 12, 14, 16. (End)
%H Michael S. Branicky, <a href="/A118514/a118514.py.txt">Python program for OEIS A118514, A118515, and A118516</a>
%H N. J. A. Sloane and others, <a href="/wiki/Sequences_of_RADD_type">Sequences of RADD type</a>, OEIS wiki.
%o (Python) # see linked program
%Y For records see A118515, A118516. Cf. A117831. S_1 is A117521.
%Y S_1013 is A120214, S_1057 is A120215, S_100013 is A120216, S_100057 is A120217, S_100103 is A120218.
%K nonn,base
%O 1,2
%A _N. J. A. Sloane_, May 06 2006
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