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A297256 Numbers whose base-5 digits have equal down-variation and up-variation; see Comments.

%I A297256 #4 Jan 15 2018 21:08:03
%S A297256 1,2,3,4,6,12,18,24,26,31,36,41,46,52,57,62,67,72,78,83,88,93,98,104,
%T A297256 109,114,119,124,126,131,136,141,146,151,156,161,166,171,176,181,186,
%U A297256 191,196,201,206,211,216,221,226,231,236,241,246,252,257,262,267
%N A297256 Numbers whose base-5 digits have equal down-variation and up-variation; see Comments.
%C A297256 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.
%H A297256 Clark Kimberling, <a href="/A297256/b297256.txt">Table of n, a(n) for n = 1..10000</a>
%e A297256 267 in base-5:  2,0,3,2, having DV = 3, UV = 3, so that 267 is in the sequence.
%t A297256 g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
%t A297256 x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
%t A297256 b = 5; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
%t A297256 w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];
%t A297256 Take[Flatten[Position[w, -1]], 120]   (* A297255 *)
%t A297256 Take[Flatten[Position[w, 0]], 120]    (* A297256 *)
%t A297256 Take[Flatten[Position[w, 1]], 120]    (* A297257 *)
%Y A297256 Cf. A297330, A297255, A297257.
%K A297256 nonn,base,easy
%O A297256 1,2
%A A297256 _Clark Kimberling_, Jan 15 2018