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A087851
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a(n)=Abs(a(n-1)-floor(n*phi)), where phi=(1+sqrt(5))/2.
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3
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1, 1, 3, 3, 5, 4, 7, 5, 9, 7, 10, 9, 12, 10, 14, 11, 16, 13, 17, 15, 18, 17, 20, 18, 22, 20, 23, 22, 24, 24, 26, 25, 28, 27, 29, 29, 30, 31, 32, 32, 34, 33, 36, 35, 37, 37, 39, 38, 41, 39, 43, 41, 44, 43, 45, 45, 47, 46, 49, 48, 50, 50, 51, 52, 53, 53, 55, 55, 56, 57, 57, 59, 59
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Suggested by Hofstadter's H-numbers A005374.
A single recursion showing chaotic behavior.
The attempt to generaize this to a(n)=Abs(a(a(n-1))-floor(n*phi)) or a(n)=Abs(a(a(a(n-1)))-floor(n*phi)) fails because a(8) is undefined.
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FORMULA
| a(1) = a(2) = 1; for n > 2, a(n) = |a(n-1)-floor(n*phi)|. - Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), Jun 16 2007
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PROG
| (TRUE BASIC) 60 REM BATRACHION SEQUENCE 61 LET gm=(1+Sqr(5))/2 70 DIM q0(0 to 4000) 80 LET q0(1)=1 90 LET q0(2)=1 91 FOR n = 3 to 201 92 LET q0(n)=Abs(q0(n-1)-int(n*gm)) 93 NEXT n 100 SET MODE "color" 110 SET WINDOW 0, 1024, 0, 750 301 PRINT" simple sequence" 302 PRINT" by Roger L. Bagula Oct 07 2003 " 381 OPEN #1: name "CM1:simple_data", create newold, org text 390 FOR x=1 to 200 391 PRINT #1: q0(x); ", "; 392 PRINT q0(x); 393 NEXT x 394 CLOSE #1 460 END
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CROSSREFS
| Cf. A005374, A087852, A087853.
A129229 is a very similar sequence.
Sequence in context: A090104 A075795 A058268 * A087852 A087853 A095334
Adjacent sequences: A087848 A087849 A087850 * A087852 A087853 A087854
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KEYWORD
| nonn
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AUTHOR
| Roger L Bagula (rlbagulatftn(AT)yahoo.com), Oct 08 2003
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Jun 18 2007
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