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%I #4 Jan 15 2018 21:08:44
%S 7,14,15,21,22,23,28,29,30,31,35,36,37,38,39,42,43,44,45,46,47,49,56,
%T 63,70,77,84,91,98,99,105,106,112,113,119,120,126,127,133,134,140,141,
%U 147,148,149,154,155,156,161,162,163,168,169,170,175,176,177,182
%N Numbers whose base-7 digits have greater up-variation than down-variation; see Comments.
%C 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 Clark Kimberling, <a href="/A297261/b297261.txt">Table of n, a(n) for n = 1..10000</a>
%e 182 in base-7: 3,5,0, having DV = 7, UV = 0, so that 182 is in the sequence.
%t g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
%t x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
%t b = 7; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
%t w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];
%t Take[Flatten[Position[w, -1]], 120] (* A297261 *)
%t Take[Flatten[Position[w, 0]], 120] (* A297262 *)
%t Take[Flatten[Position[w, 1]], 120] (* A297263 *)
%Y Cf. A297330, A297262, A297263.
%K nonn,base,easy
%O 1,1
%A _Clark Kimberling_, Jan 15 2018
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