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

Author

Scott R. Shannon, Apr 26 2020

Keywords

• nonn
• base

Comments

To obtain the difference version of the 'Decade transform' of n first 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. See the Examples for details.

See A330859 for the additive version of the same transform.

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.

Crossrefs

Cf. A330859, A011557, A040115, A053392.