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%I #4 Feb 03 2018 16:36:47
%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,0,
%T 0,0,1,2,3,4,5,6,7,8,9,10,11,12,13,0,0,0,0,1,2,3,4,5,6,7,8,9,10,11,12,
%U 0,0,0,0,0,1,2,3,4,5,6,7,8,9,10,11,0,0,0
%N Up-variation of the 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). Every positive integer occurs infinitely many times. See A297330 for a guide to related sequences and partitions of the natural numbers.
%H Clark Kimberling, <a href="/A297247/b297247.txt">Table of n, a(n) for n = 1..10000</a>
%e 20 in base 16: 1,4; here UV = 3, so that a(20) = 3.
%t g[n_, b_] := Differences[IntegerDigits[n, b]];
%t b = 16; z = 120; Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}]; (* A297246 *)
%t Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}]; (* A297247 *)
%Y Cf. A297246, A297248, A297330.
%K nonn,base,easy
%O 1,19
%A _Clark Kimberling_, Jan 18 2018
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