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%I #19 Jan 30 2023 12:26:19
%S 1,0,1,2,3,4,5,6,7,8,2,1,0,1,2,3,4,5,6,7,3,2,1,0,1,2,3,4,5,6,4,3,2,1,
%T 0,1,2,3,4,5,5,4,3,2,1,0,1,2,3,4,6,5,4,3,2,1,0,1,2,3,7,6,5,4,3,2,1,0,
%U 1,2,8,7,6,5,4,3,2,1,0,1,9,8,7,6,5,4,3,2,1,0,1,0,1,1,1,2,1,3,1,4,1,5
%N List of absolute values of differences between digits of 10, 11, 12, ..., listed digit by digit.
%C Start with the empty sequence. For n = 10, 11, 12, ... do the following. Let the decimal expansion of n be abcd...efg, say. Append the numbers |a-b|, |b-c|, |c-d|, ... |e-f|, |f-g| to the sequence.
%C The offset is slightly misleading since for n > 99 the index n is in no direct relation with the number whose digits are used to produce a(n), in contrast to A040115 where all digit-differences of n are concatenated, and leading zeros don't appear. For example, a(100) = 1 and a(101) = 0 are the two differences between the digits of 100. Similarly, a(100 + 2k) corresponds to the difference between first and second digit of 100 + k. Therefore, a(120) = 0. - _M. F. Hasler_, Nov 09 2019
%H T. D. Noe, <a href="/A040114/b040114.txt">Table of n, a(n) for n = 10..1902</a>
%e From _M. F. Hasler_, Nov 09 2019: (Start)
%e The first term is the difference between digits of 10, which is 1.
%e The second term is the difference between digits of 11, which is 0.
%e The 100th term is the difference between the first two digits of 100, 1-0 = 1.
%e The 101st term is the difference between the last two digits of 100, 0-0 = 0.
%e The 120th term is the difference between the first two digits of 110, 1-1 = 0: Here "leading zeros" are preserved, in contrast to A040115 where all digit-wise differences of any n are concatenated to one term, and leading zeros disappear.
%e (End)
%e When we reach n = 371, for example, we append 4 and 6 to the sequence.
%t Flatten[Table[Abs[Differences[IntegerDigits[n]]],{n,10,200}]] (* _Harvey P. Dale_, Jun 28 2021 *)
%Y Cf. A037904, A040115, A040163, A040997.
%K nonn,base,less
%O 10,4
%A _Felice Russo_
%E Definition clarified by _N. J. A. Sloane_, Aug 19 2008.
%E Name edited by _M. F. Hasler_, Nov 09 2019
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