A334387 The difference version of the 'Decade transform' : to obtain a(n) write n as a sum of its power-of-ten parts and then continue to calculate the absolute value of the difference between the adjacent parts until a single number remains.
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 70, 69, 68
Offset: 0
Examples
Let n = 32871. Write n as a sum of its power-of-ten parts: 32871 = 30000+2000+800+70+1 Now take the absolute value of the difference between the adjacent numbers in this sum: 30000+2000+800+70+1 -> (|30000-2000|):(|2000-800|):(|800-70|):(|70-1|) = 28000:1200:730:69 Now repeat this until a single number remains: 28000:1200:730:69 -> 26800:470:661 26800:470:661 -> 26330:191 26330:191 -> 26139 Thus a(32871) = 26139. Other examples: a(11) = 9 as 11 = 10+1 thus 10:1 -> 9. a(19) = 1 as 19 = 10+9 thus 10:9 -> 1. a(20) = 20 as 20 = 20+0 thus 20:0 -> 20. a(67) = 53 as 67 = 60+7 thus 60:7 -> 53. a(1234) = 486 as 1234 = 1000+200+30+4 thus 1000:200:30:4 -> 800:170:26 -> 630:144 -> 486. a(15010) = 0 as 15010 = 10000+5000+0+10+0 thus 10000:5000:0:10:0 -> 5000:5000:10:10 -> 0:4990:0 -> 4990:4990 -> 0.
Links
- Scott R. Shannon, Line graph of the terms for n=0 to 1000000.
Comments