A334387 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

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.

LINKS

Table of n, a(n) for n=0..72.

Scott R. Shannon, Line graph of the terms for n=0 to 1000000.

EXAMPLE

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