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Search: id:A004000
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| A004000 |
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RATS: Reverse Add Then Sort the digits applied to previous term, starting with 1.
(Formerly M1137)
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+0
12
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| 1, 2, 4, 8, 16, 77, 145, 668, 1345, 6677, 13444, 55778, 133345, 666677, 1333444, 5567777, 12333445, 66666677, 133333444, 556667777, 1233334444, 5566667777, 12333334444, 55666667777, 123333334444, 556666667777, 1233333334444
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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It is conjectured that no matter what the starting term is, repeatedly applying RATS leads either to this sequence or into a cycle of finite length, such as those in A066710 and A066711.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. K. Guy, Conway's RATS and other reversals, Amer. Math. Monthly, 96 (1989), 425-428.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..200
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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Let a(n) = k, form m by Reversing the digits of k, Add m to k Then Sort the digits of the sum into increasing order to get a(n+1).
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EXAMPLE
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668 -> 668 + 866 = 1534 -> 1345.
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MAPLE
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read transforms; RATS := n -> digsort(n + digrev(n)); b := [1]; t := [1]; for n from 1 to 50 do t := RATS(t); b := [op(b), t]; od: b;
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PROGRAM
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(MAGMA) [ n eq 1 select 1 else Seqint(Reverse(Sort(Intseq(p + Seqint(Reverse(Intseq(p))) where p is Self(n-1))))) : n in [1..10]]; - from Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006
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CROSSREFS
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Cf. A036839, A066710, A066711, A066713.
Sequence in context: A012997 A013184 A066713 this_sequence A051300 A001127 A051299
Adjacent sequences: A003997 A003998 A003999 this_sequence A004001 A004002 A004003
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KEYWORD
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base,nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Entry revised Jan 19 2002
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