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A101210
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Charlie Chaplin numbers: Stage 1: the input is the sequence F(n) = 1,2,1,2,1,2,1,2,... of alternating 1's and 2s, starting with F(1)=1. Let m = 1. At each iteration take F(m) and add it to F(m+F(m)) then increment m by 1 and repeat. The numbers are the values of F(m) which are larger than all previous values.
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2
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1, 3, 4, 5, 8, 11, 12, 13, 14, 15, 16, 17, 23, 33, 37, 39, 68, 73, 76, 79, 85, 90, 97, 117, 157, 160, 180, 252, 253, 368, 376, 378, 381, 421, 429, 534, 644, 652, 657, 742, 743, 746, 839, 890, 1026, 1329, 1344, 1345, 1523, 1526, 1545, 1546, 1547, 1550, 1562
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OFFSET
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1,2
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COMMENTS
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Charlie Chaplin numbers are inspired by his comedy routine working on a conveyor belt. Which input functions give chaotic outputs? How does the output sequence grow?
Comment from David Wasserman, Mar 11 2008: The sequence gives the record values of the system output. The record values that occur while computing the system output are given in A116587.
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LINKS
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MAPLE
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A101210 := proc(nmax) local F, m, Fnew, Fnewidx, a ; F := [seq(2- (i mod 2), i=1..nmax)] ; m := 1: while m <= nops(F) do if m+op(m, F) <= nops(F) then Fnew := op(m, F)+op(m+op(m, F), F) ; Fnewidx := m+op(m, F) ; F := subsop(Fnewidx=Fnew, F) ; fi ; m := m+1 ; od: a := [1] ; for m from 2 to nops(F) do if op(m, F) > op(-1, a) then a := [op(a), op(m, F)] ; fi ; od: a ; end: A101210(40000) ; # R. J. Mathar, Mar 12 2008
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MATHEMATICA
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max = 50000; chCh = Flatten[Table[{1, 2}, {max}]]; iter = 1; While[iter < max/2, chCh[[iter + chCh[[iter]]]] += chCh[[iter]]; iter++]; currHigh=1; jter=2; While[jter <= Length[chCh], If[chCh[[jter]] > currHigh, currHigh = chCh[[jter]]; jter++, chCh = Drop[chCh, {jter}]]]; chCh = Drop[chCh, -1] (* Alonso del Arte, Dec 03 2011 *)
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CROSSREFS
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KEYWORD
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easy,nonn,obsc
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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