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A297261 Numbers whose base-7 digits have greater down-variation than up-variation; see Comments.

%I A297261 #13 Dec 26 2024 14:36:03
%S A297261 7,14,15,21,22,23,28,29,30,31,35,36,37,38,39,42,43,44,45,46,47,49,56,
%T A297261 63,70,77,84,91,98,99,105,106,112,113,119,120,126,127,133,134,140,141,
%U A297261 147,148,149,154,155,156,161,162,163,168,169,170,175,176,177,182
%N A297261 Numbers whose base-7 digits have greater down-variation than up-variation; see Comments.
%C A297261 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 A297261 Clark Kimberling, <a href="/A297261/b297261.txt">Table of n, a(n) for n = 1..10000</a>
%e A297261 182 in base-7:  3,5,0, having DV = 5, UV = 2, so that 182 is in the sequence.
%t A297261 g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
%t A297261 x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
%t A297261 b = 7; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
%t A297261 w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];
%t A297261 Take[Flatten[Position[w, -1]], 120]   (* A297261 *)
%t A297261 Take[Flatten[Position[w, 0]], 120]    (* A297262 *)
%t A297261 Take[Flatten[Position[w, 1]], 120]    (* A297263 *)
%Y A297261 Cf. A297330, A297262, A297263.
%K A297261 nonn,base,easy
%O A297261 1,1
%A A297261 _Clark Kimberling_, Jan 15 2018
%E A297261 Name corrected by _Ray Goldman_, Aug 10 2024