# [seqfan] Mini-max numbers

Fri May 10 19:11:08 CEST 2013

```Dear SeqFans,

Let, for n>=3, N be n-digit number such that the first zeros are allowed but not all digits are the same. Let consider digits of N in non-increasing order and the corresponding number denote by N_max; after that we consider digits of N in non-decreasing order and the corresponding number denote by N_min. If N_max-N_min=N, then we call N a mini-max number of cycle 1; if N_max-N_min=N_1 which differs of N, but (N_1)_max-(N_1)_min=N, then we call N a mini-max number of cycle 2, etc.
By handy, I found the following numbers:
If n=3, N=495 is a mini-max number of cycle 1. Indeed, 954-459=495;
If n=4, N=6174 is a mini-max number of cycle 1. Indeed, 7641-1467=6174;
If n=5, N=53955 is a mini-max number of cycle 2, since N_1=95553-35559=59994 and N_2=99954-45999=53955=N;
If n=6, N=840852 is a mini-max number of cycle 7, since N_1=885420-024588=860832;  N_2=886320-023688=862632;
N_3=866322-223668=642654; N_4=665442-244566=420876; N_5=876420-024678=851742; N_6=875421-124578=750843; N_7=875430-034578=840852=N.
It is interesting to find for every n the set of mini-max numbers with their cycles. Are mini-max numbers known, maybe, under another name?

Best regards,