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A117816
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Let T_n be the infinite sequence formed by starting with 1 and repeatedly reversing the digits and adding n to get the next term. Sequence gives number of steps for T_n to enter a cycle, or -1 if no cycle is ever reached.
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72
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1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 2, 31, 15, -1, 721, 9, 1, 6, -1, 3, 5, 28, 29, 131, 23, 1, 31, 6, -1, 1, 19, 1, 53, 4, 406, 34, 254, 8, -1, 3, 245, 1, 3, 2, 422, 42, 308, 1, -1, 2, 2, 49, 1, 1371, 13, 1, 1, 2, -1, 78, 65, 1, 809, 1575, 5, 43, 31, 2, -1, 33, 2, 21, 192, 857, 91, 1, 2, 2, -1, 2, 491, 1, 2, 1, 81, 49, 1, 2, -1, 35, 197, 72, 1, 12, 79, 1, 6004, 1, -1, 52, 10264, 9, 28, 2, 2, 1, 427, 1, -1, 1, 1, 49, 167
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,12
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COMMENTS
| Comments following discussions with David Applegate (david(AT)research.att.com), May 05, 2006: Certainly a(10) = -1 and probably a(n) is always -1 if n is a multiple of 10. Furthermore a(15) is almost certainly -1: T_15 has not reached a cycle in 10^7 terms (see A118532).
Comment from Martin Fuller, May 12 2006: If n is a multiple of 10 the operation can never generate a trailing zero and so is reversible. So it loops only if it returns to the start, which is impossible. Hence a(10k) = -1.
Comment from Martin Fuller, May 12 2006: I suspect a(115) = 385592406, A117817(115) = 79560. Can someone confirm?
The -1 entries for n >= 0 both here and in A117817 are presently only conjectural.
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LINKS
| N. J. A. Sloane, Sequences of RADD type
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EXAMPLE
| T_2 enters a cycle of length 81 after 1 step.
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MATHEMATICA
| ReverseNum[n_] := FromDigits[Reverse[IntegerDigits[n]]]; maxLen=10000; Table[z=1; lst={1}; While[z=ReverseNum[z]+n; !MemberQ[lst, z] && Length[lst]<maxLen, AppendTo[lst, z]]; If[Length[lst]<maxLen, Position[lst, z][[1, 1]]-1, -1], {n, 100}] (Noe)
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CROSSREFS
| For T_1, T_2, ..., T_16 (omitting T_9, which is uninteresting) see A117230, A117521, A118517, A117828, A117800, A118525, A118526, A118527, A117841, A118528, A118529, A118530, A118531, A118532, A118533.
Cf. A117817.
Sequence in context: A159578 A178194 A069460 * A099189 A053234 A020896
Adjacent sequences: A117813 A117814 A117815 * A117817 A117818 A117819
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KEYWORD
| sign,base
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), following discussions with Luc Stevens, May 04 2006
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EXTENSIONS
| a(21)-a(33) from Luc Stevens, May 08 2006
a(33) onwards from T. D. Noe (noe(AT)sspectra.com), May 10 2006
Further terms from Martin Fuller, May 12 2006
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