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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. 2
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

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: A213651 A287796 A073835 * A051503 A331375 A179622

Adjacent sequences:  A334384 A334385 A334386 * A334388 A334389 A334390

KEYWORD

nonn,base

AUTHOR

Scott R. Shannon, Apr 26 2020

STATUS

approved

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Last modified June 13 13:40 EDT 2021. Contains 344999 sequences. (Running on oeis4.)