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

0,3

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
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.

Crossrefs

Cf. A330859, A011557, A040115, A053392.

Sequence in context: A287796 A355675 A073835 * A051503 A331375 A179622

Adjacent sequences: A334384 A334385 A334386 * A334388 A334389 A334390

Keyword

nonn,base

Author

Scott R. Shannon, Apr 26 2020

Status

approved