A235335 Evolution of 13094 using Eric Angelini's add-or-subtract-and-iterate procedure.

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

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

Hans Havermann, Table of n, a(n) for n = 1..10000

Eric Angelini, Add or subtract the result. Iterate.

E. Angelini, Add or subtract the result. Iterate. [Cached copy, with permission]

Hans Havermann, 13094

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

Sequence in context: A165679 A111887 A249495 * A184768 A345150 A345151

Adjacent sequences: A235332 A235333 A235334 * A235336 A235337 A235338

Keyword

nonn,base,nice

Author

Hans Havermann, Jan 06 2014

Status

approved