Hello Math-Fun, The Seven+ operation transforms a digit 7 into a plus sign. The integer 170 becomes 1+0 which is 1. We want that a(n), transformed by the Seven+ operation, divides a(n+1). The term a(n+1) has to contain at least one digit 7. No two identical terms in the sequence S – which should be the lexico-first of its kind. For a(1) = 170, we get: S = 170, 171, 172, 174, 175, 270, 176, 273, 275, 371, 272, 276, 376, 279, 374, 378, 473, 476, 370,... We see indeed that: 170 = 1+0 = 1 divides 171; 171 = 1+1 = 2 divides 172; 172 = 1+2 = 3 divides 174; 174 = 1+4 = 5 divides 175; 175 = 1+5 = 6 divides 270; etc. Numbers we don't want to see in S: — no term starting with a 7 (ex. 754 or 7574); — no term ending with a 7 (ex. 127 or 1727); — no term with 2 or more consecutive 7 (ex. 1778); — between two 7, no string with a leading 0 (ex. 170578 – but 17078 is ok as this term would produce 9). Where does S (S for "seven") go? As usual, please forgive my hand mistakes. Best, É. Nothing more on my personal web page: http://cinquantesignes.blogspot.com/2020/05/seven-plus.html