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Search: id:A118514
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| A118514 |
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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. |
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10
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| 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, 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, 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
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OFFSET
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1,2
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COMMENT
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Initial cycles have length 81 or 90.
There is one cycle of length 81 (least component is 3, all components have at most three digits, cf. 117521), 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 (klaus-brockhaus(AT)t-online.de), Jun 10 2006
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LINKS
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N. J. A. Sloane, Sequences of RADD type
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CROSSREFS
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For records see A118515, A118516. Cf. A117831. S_1 is A117521.
S_1013 is A120214, S_1057 is A120215, S_100013 is A120216, S_100057 is A120217, S_100103 is A120218.
Sequence in context: A022695 A067169 A011339 this_sequence A059339 A092735 A035464
Adjacent sequences: A118511 A118512 A118513 this_sequence A118515 A118516 A118517
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KEYWORD
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nonn,base
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AUTHOR
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njas, May 06 2006
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