Hello SeqFan and Math-fun, Let's start with an example of "sliding number": 1/4 + 1/25 = 0.29 --> 29 is a "sliding number" 1/8 + 1/125 = 0.133 --> 133 is a "sliding number" 1/2 + 1/5 = 0.7 --> 7 is a "sliding number" etc. Note that : 1/20 + 1/50 = 0.70 --> 70 is a "sliding number" though 0.70 is usually written 0.7 So any "sliding number" G produces an infinite quantity of others : Gx10, Gx100, Gx1000, etc. Generally speaking we have this: 1/a + 1/b = (a+b)/10^k [with k=1,=2,=3,=4, ...] --> the "sliding number" G = a+b My pb is to build a correct seq. of G's (how not to forget any G behind?) By hand I've proceeded so: 10 --> 1+10 --> G(2)=11 2+5 --> G(1)=7 100 --> 1+100 --> G(7)=101 2+50 --> G(6)=52 4+25 --> G(5)=29 5+20 --> G(4)=25 10+10 --> G(3)=20 1000 --> 1+1000 --> G(15)=1001 2+500 --> G(14)502 4+250 --> G(13)=254 5+200 --> G(12)=205 8+125 --> G(11)133 10+100 --> G(10)=110 20+50 --> G(9)=70 25+40 --> G(8)=65 ... but you see now my pb: G(8) and G(9) are < G(7) ! I have to rename them... The sequence would then start like this: 7,11,20,25,29,52,65,70,101,110,133,205... BUT: 10000 --> 100+100 (among others) which gives G=200... So I have to correct the sequence and insert 200: 7,11,20,25,29,52,65,70,101,110,133,200,205... [BTW 200 is G(3)x10] Could someone compute enough terms to be submitted to the OEIS without leaving any G integer behind? Many thanks, É. ----------- PS. I don't know who has given the name "sliding numbers" to those integers -- I might have read that on the Internet somewhere around 1997...