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%I #4 Jan 17 2018 17:52:18
%S 0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,3,4,5,6,7,8,9,10,11,2,1,0,1,2,3,4,5,
%T 6,7,8,9,10,3,2,1,0,1,2,3,4,5,6,7,8,9,4,3,2,1,0,1,2,3,4,5,6,7,8,5,4,3,
%U 2,1,0,1,2,3,4,5,6,7,6,5,4,3,2,1,0,1
%N Total variation of base-13 digits of n; see Comments.
%C Suppose that a number n has base-b digits b(m), b(m-1), ..., b(0). The base-b down-variation of n is the sum DV(n,b) of all d(i)-d(i-1) for which d(i) > d(i-1); the base-b up-variation of n is the sum UV(n,b) of all d(k-1)-d(k) for which d(k) < d(k-1). The total base-b variation of n is the sum TV(n,b) = DV(n,b) + UV(n,b). See A297330 for a guide to related sequences and partitions of the natural numbers:
%H Clark Kimberling, <a href="/A297239/b297239.txt">Table of n, a(n) for n = 1..10000</a>
%e 2^20 in base 13: 2, 10, 9, 3, 7, 9; here, DV = 12 and UV = 9, so that a(2^20) = 21.
%t b = 13; z = 120; t = Table[Total@Flatten@Map[Abs@Differences@# &, Partition[IntegerDigits[n, b], 2, 1]], {n, z}] (* cf. Michael De Vlieger, e.g. A037834 *)
%Y Cf. A297237, A297238, A297330.
%K nonn,base,easy
%O 1,16
%A _Clark Kimberling_, Jan 17 2018
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