|
| |
|
|
A235335
|
|
Evolution of 13094 using Eric Angelini's add-or-subtract-and-iterate procedure.
|
|
1
|
|
|
|
13094, 37047, 84481, 44004, 39964, 100285, 202919, 430806, 291944, 1080446, 2964471, 10284832, 22929343, 15153232, 59574343, 15343231, 57454351, 34343107, 23230933, 12091332, 25073343, 60813454, 129534566, 303745671, 638056833, 279544330, 803645362, 1636857708
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
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.
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.
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.
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
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.
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.
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.
|
|
|
MATHEMATICA
|
f[p_] := (d=IntegerDigits[p]; r=RotateLeft[d]; q=FromDigits[Abs[d-r]]; If[q>p, p+q, p-q])
NestList[f, 13094, 100000]
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,base,nice
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
