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%I #16 Jun 10 2016 00:21:00
%S 13094,37047,84481,44004,39964,100285,202919,430806,291944,1080446,
%T 2964471,10284832,22929343,15153232,59574343,15343231,57454351,
%U 34343107,23230933,12091332,25073343,60813454,129534566,303745671,638056833,279544330,803645362,1636857708
%N Evolution of 13094 using Eric Angelini's add-or-subtract-and-iterate procedure.
%C The procedure: Start with decimal number p. From left to right, determine the absolute differences between p's adjacent digits (ending with the last digit of p minus the first digit). Concatenate these differences to create decimal number q. If q > p, compute p + q. If q < p, compute p - q. Either way, this is our new p. Repeat.
%C 13094 is the smallest number not known to enter a cycle. Phil Carmody has calculated more than 150*10^6 iterations, resulting in a number with more than 210000 digits.
%C Under the procedure some numbers (199, 10853, 10886, ..) require many iterations before entering a cycle. Cycles may be quite lengthy: 204099163 is the smallest member of a size-868 cycle.
%H Hans Havermann, <a href="/A235335/b235335.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/AddOrSubtract.htm">Add or subtract the result. Iterate.</a>
%H E. Angelini, <a href="/A235335/a235335.pdf">Add or subtract the result. Iterate.</a> [Cached copy, with permission]
%H Hans Havermann, <a href="http://gladhoboexpress.blogspot.ca/2012/10/13094.html">13094</a>
%e p = 13094; |1-3|=2, |3-0|=3, |0-9|=9, |9-4|=5, |4-1|=3; q = 23953; q > p so new p is p + q = 37047.
%e p = 37047; |3-7|=4, |7-0|=7, |0-4|=4, |4-7|=3, |7-3|=4; q = 47434; q > p so new p is p + q = 84481.
%e p = 84481; |8-4|=4, |4-4|=0, |4-8|=4, |8-1|=7, |1-8|=7; q = 40477; q < p so new p is p - q = 44004.
%t f[p_] := (d=IntegerDigits[p]; r=RotateLeft[d]; q=FromDigits[Abs[d-r]]; If[q>p,p+q,p-q])
%t NestList[f,13094,100000]
%K nonn,base,nice
%O 1,1
%A _Hans Havermann_, Jan 06 2014
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