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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.

%I A334387 #28 May 14 2020 15:59:51
%S A334387 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,
%T A334387 11,30,29,28,27,26,25,24,23,22,21,40,39,38,37,36,35,34,33,32,31,50,49,
%U A334387 48,47,46,45,44,43,42,41,60,59,58,57,56,55,54,53,52,51,70,69,68
%N 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.
%C A334387 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.
%C A334387 See A330859 for the additive version of the same transform.
%H A334387 Scott R. Shannon, <a href="/A334387/a334387.png">Line graph of the terms for n=0 to 1000000</a>.
%e A334387 Let n = 32871. Write n as a sum of its power-of-ten parts:
%e A334387 32871 = 30000+2000+800+70+1
%e A334387 Now take the absolute value of the difference between the adjacent numbers in this sum:
%e A334387 30000+2000+800+70+1 -> (|30000-2000|):(|2000-800|):(|800-70|):(|70-1|) = 28000:1200:730:69
%e A334387 Now repeat this until a single number remains:
%e A334387 28000:1200:730:69 -> 26800:470:661
%e A334387 26800:470:661 -> 26330:191
%e A334387 26330:191 -> 26139
%e A334387 Thus a(32871) = 26139.
%e A334387 Other examples:
%e A334387 a(11) = 9 as 11 = 10+1 thus 10:1 -> 9.
%e A334387 a(19) = 1 as 19 = 10+9 thus 10:9 -> 1.
%e A334387 a(20) = 20 as 20 = 20+0 thus 20:0 -> 20.
%e A334387 a(67) = 53 as 67 = 60+7 thus 60:7 -> 53.
%e A334387 a(1234) = 486 as 1234 = 1000+200+30+4 thus 1000:200:30:4 -> 800:170:26 -> 630:144 -> 486.
%e A334387 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.
%Y A334387 Cf. A330859, A011557, A040115, A053392.
%K A334387 nonn,base
%O A334387 0,3
%A A334387 _Scott R. Shannon_, Apr 26 2020