SMI (Split, Multiply, Iterate)
The SMI operation is based on the “persistence of a number” idea: https://oeis.org/A031346 See also: http://neilsloane.com/doc/persistence.html Here, we always split the integer N into two integers, then multiply them (and iterate). 2023 can thus be split into 20 and 23 (producing 20*23 = 460), or split into 202 and 3 (producing 202*3 = 606). The split 2 and 023 is forbidden, as 023 is not an integer (but 460 can be split into 46 and 0 as 0 is an integer). To explore the SMI operation, my friend Nicolas Graner has built this (wonderful) tool: http://graner.name/nicolas/divers/reduction.php This tool explains how I “computed” the hereunder sequences. All typos, mistakes, errors, omissions… are my fault and not that of Nicolas' engine. Numbers reachin g 0 : SMI 0 = 0,10,20,25,30,40,45,50,52,54,55,56,58,59,60,65,69,70,78,80,85,87,90,95,96,100,101,102,103,104,105,106,107,108,109,110,115,… We see that 115 reaches 0 when split into 11*5: 11*5 = 55 –> 5*5 = 25 –