Concatenating two multiplications
Today we'll explore the rules for a new (?) iteration a ) take any number N (say 10234567890) b ) replace all the zeros of N by ones (we get 11234567891) c ) make now the "O" multiplication (we multiply the odd digits; O = 1*1*3*5*7*9*1 = 945) d ) make now the "E" multiplication (we multiply the even digits; E = 2*4*6*8 = 384) e ) form the new number N using the concatenation OE (here N = 945384) and iterate; f ) if this leads to a single-digit N, or a 2-digit N like 12 or 21 (one odd digit, one even), square N and iterate. Example with the avatars of 12 12 --> 144 (we have squared 12) 144 --> 116 (we did 4*4 = 16) 116 --> 16 (we did 1*1 = 1) 16 --> 256 (we have squared 16) 256 --> 512 (we did 2*6 = 12, concatenated to 5) 512 --> 52 (we did 5*1 = 1) 52 --> 2704 (we have squared 52) 2704 --> 2714 (we have replaced 0 by 1) 2714 --> 78 (we did 7*1 = 7 and concatenated 8 =2*4) 78 --> 6084 (we have squared 78