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A101210 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. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

LINKS

David Wasserman and Paul Tek, Table of n, a(n) for n = 1..1000 (first 79 terms from David Wasserman)

MAPLE

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

MATHEMATICA

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 *)

CROSSREFS

Cf. A116587.

Sequence in context: A228305 A103329 A080726 * A206445 A047599 A050846

Adjacent sequences:  A101207 A101208 A101209 * A101211 A101212 A101213

KEYWORD

easy,nonn,obsc

AUTHOR

Gordon Hamilton, Dec 14 2004

EXTENSIONS

More terms from David Wasserman, Mar 11 2008

More terms from R. J. Mathar, Mar 12 2008

STATUS

approved

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Last modified March 19 04:17 EDT 2019. Contains 321311 sequences. (Running on oeis4.)