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%I #4 Jan 17 2018 17:52:43
%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,2,
%T 1,0,1,2,3,4,5,6,7,8,9,10,11,12,13,3,2,1,0,1,2,3,4,5,6,7,8,9,10,11,12,
%U 4,3,2,1,0,1,2,3,4,5,6,7,8,9,10,11,5,4,3
%N Total variation of base-16 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="/A297248/b297248.txt">Table of n, a(n) for n = 1..10000</a>
%e 3^10 in base 16: 14, 6, 10, 9; here, DV = 9 and UV = 4, so that a(2^20) = 13.
%t b = 16; 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. A297246, A297247, A297330.
%K nonn,base,easy
%O 1,19
%A _Clark Kimberling_, Jan 17 2018
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