cp's OEIS Frontend

A297231 Down-variation of the base-11 digits of n; see Comments.

%I A297231 #9 Jan 19 2018 02:21:18
%S A297231 0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,2,1,0,0,0,0,0,0,0,0,0,3,2,
%T A297231 1,0,0,0,0,0,0,0,0,4,3,2,1,0,0,0,0,0,0,0,5,4,3,2,1,0,0,0,0,0,0,6,5,4,
%U A297231 3,2,1,0,0,0,0,0,7,6,5,4,3,2,1,0,0,0
%N A297231 Down-variation of the base-11 digits of n; see Comments.
%C A297231 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 A297231 Clark Kimberling, <a href="/A297231/b297231.txt">Table of n, a(n) for n = 1..10000</a>
%e A297231 22 in base 11: 2,0; here DV = 2, so that a(22) = 2.
%t A297231 g[n_, b_] := Differences[IntegerDigits[n, b]];
%t A297231 b = 11; z = 120; Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}];  (* A297231 *)
%t A297231 Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}]; (* A297232 *)
%Y A297231 Cf. A297232, A297233, A297330.
%K A297231 nonn,base,easy
%O A297231 1,22
%A A297231 _Clark Kimberling_, Jan 17 2018