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A297238 Up-variation of the base-13 digits of n; see Comments.

%I A297238 #7 Jan 19 2018 16:23:25
%S A297238 0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,4,5,6,7,8,9,10,11,0,0,0,1,2,3,4,5,
%T A297238 6,7,8,9,10,0,0,0,0,1,2,3,4,5,6,7,8,9,0,0,0,0,0,1,2,3,4,5,6,7,8,0,0,0,
%U A297238 0,0,0,1,2,3,4,5,6,7,0,0,0,0,0,0,0,1
%N A297238 Up-variation of the base-13 digits of n; see Comments.
%C A297238 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 A297238 Clark Kimberling, <a href="/A297238/b297238.txt">Table of n, a(n) for n = 1..10000</a>
%e A297238 17 in base 13: 1,4; here UV = 3, so that a(17) = 3.
%t A297238 g[n_, b_] := Differences[IntegerDigits[n, b]];
%t A297238 b = 13; z = 120; Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}];  (* A297237 *)
%t A297238 Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}]; (* A297238 *)
%Y A297238 Cf. A297237, A297239, A297330.
%K A297238 nonn,base,easy
%O A297238 1,16
%A A297238 _Clark Kimberling_, Jan 17 2018