OFFSET
10,1
COMMENTS
The smallest integers such that the number of iterations equals 1, 2, 3, ... are 19, 14, 22, 11, 10, 104, 106, 110, 119, 108, 112, 101, 100, 114, 121, 502, 1041, 1402, 10110, 10048, 10010, 10202, 10113, 10116, 10118, 10026, 11294, 10281, 10282, 10120, ...
LINKS
Michel Lagneau, Table of n, a(n) for n = 10..10000
EXAMPLE
a(10) = 5 because 10 -> 11 -> 22 -> 44 -> 88 -> 66 with 5 iterations where 66 is the last number of the cycle because 66 -> 22, which has already appeared in the trajectory.
a(327) = 9 because 327 -> 590 -> 495 -> 349 -> 732 -> 59 -> 44 -> 88 -> 66 -> 22 with 9 iterations where 22 is the last number of the cycle because 22 -> 44, which has already appeared in the trajectory.
MAPLE
with(numtheory):nn:=100:for n from 10 to 200 do:lst:={n}:nn:=n:s:=1:for it from 1 to 40 while (s<>0)do: x:=convert(nn, base, 10):n1:=nops(x):s:=sum('irem(x[i]+x[i+1], 10)*10^i', 'i'=1..n1-1):s:=s+irem(x[n1]+x[1], 10):lst:=lst union {s}:nn:=s:od:n2:=nops(lst)-1: printf(`%d, `, n2):od:
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Michel Lagneau, Feb 09 2014
EXTENSIONS
Name edited by Jon E. Schoenfield, Sep 12 2017
STATUS
approved