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A297286 Numbers whose base-15 digits have equal down-variation and up-variation; see Comments.

%I A297286 #8 Jan 23 2018 20:32:25
%S A297286 1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,32,48,64,80,96,112,128,144,160,
%T A297286 176,192,208,224,226,241,256,271,286,301,316,331,346,361,376,391,406,
%U A297286 421,436,452,467,482,497,512,527,542,557,572,587,602,617,632,647
%N A297286 Numbers whose base-15 digits have equal down-variation and up-variation; see Comments.
%C A297286 Suppose that 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 the guide at A297330.
%C A297286 Differs from A029960 after the zero first for 3391 = 1011_15, which is not in A029960 but in this sequence. - _R. J. Mathar_, Jan 23 2018
%H A297286 Clark Kimberling, <a href="/A297286/b297286.txt">Table of n, a(n) for n = 1..10000</a>
%e A297286 647 in base-15:  2,13,2 having DV = 11, UV = 11, so that 647 is in the sequence.
%t A297286 g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
%t A297286 x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
%t A297286 b = 15; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
%t A297286 w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];
%t A297286 Take[Flatten[Position[w, -1]], 120]   (* A297285 *)
%t A297286 Take[Flatten[Position[w, 0]], 120]    (* A297286 *)
%t A297286 Take[Flatten[Position[w, 1]], 120]    (* A297287 *)
%Y A297286 Cf. A297330, A297285, A297287.
%K A297286 nonn,base,easy
%O A297286 1,2
%A A297286 _Clark Kimberling_, Jan 17 2018