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A297262 Numbers whose base-7 digits have equal up-variation and down-variation; see Comments.

%I A297262 #4 Jan 16 2018 11:31:22
%S A297262 1,2,3,4,5,6,8,16,24,32,40,48,50,57,64,71,78,85,92,100,107,114,121,
%T A297262 128,135,142,150,157,164,171,178,185,192,200,207,214,221,228,235,242,
%U A297262 250,257,264,271,278,285,292,300,307,314,321,328,335,342,344,351,358
%N A297262 Numbers whose base-7 digits have equal up-variation and down-variation; see Comments.
%C A297262 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 A297262 Clark Kimberling, <a href="/A297262/b297262.txt">Table of n, a(n) for n = 1..10000</a>
%e A297262 358 in base-7:  1,0,2,1, having DV = 2, UV = 2, so that 358 is in the sequence.
%t A297262 g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
%t A297262 x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
%t A297262 b = 7; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
%t A297262 w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];
%t A297262 Take[Flatten[Position[w, -1]], 120]   (* A297261 *)
%t A297262 Take[Flatten[Position[w, 0]], 120]    (* A297262 *)
%t A297262 Take[Flatten[Position[w, 1]], 120]    (* A297263 *)
%Y A297262 Cf. A297330, A297261, A297263.
%K A297262 nonn,base,easy
%O A297262 1,2
%A A297262 _Clark Kimberling_, Jan 15 2018