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A297282 Numbers whose base-14 digits have greater down-variation than up-variation; see Comments.

%I A297282 #8 Jan 23 2018 20:09:33
%S A297282 14,28,29,42,43,44,56,57,58,59,70,71,72,73,74,84,85,86,87,88,89,98,99,
%T A297282 100,101,102,103,104,112,113,114,115,116,117,118,119,126,127,128,129,
%U A297282 130,131,132,133,134,140,141,142,143,144,145,146,147,148,149,154
%N A297282 Numbers whose base-14 digits have greater down-variation than up-variation; see Comments.
%C A297282 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 A297282 Differs from A296755 first for 224 = 120_14, which is in this sequence because DV(224,14) = 2 > UV(224,14)=1, but not in A296755 because the number of rises equals the number of falls. - _R. J. Mathar_, Jan 23 2018
%H A297282 Clark Kimberling, <a href="/A297282/b297282.txt">Table of n, a(n) for n = 1..10000</a>
%e A297282 154 in base-14:  11,0 having DV = 9, UV = 0, so that 154 is in the sequence.
%t A297282 g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
%t A297282 x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
%t A297282 b = 14; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
%t A297282 w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];
%t A297282 Take[Flatten[Position[w, -1]], 120]   (* A297282 *)
%t A297282 Take[Flatten[Position[w, 0]], 120]    (* A297283 *)
%t A297282 Take[Flatten[Position[w, 1]], 120]    (* A297284 *)
%Y A297282 Cf. A297330, A297283, A297284.
%K A297282 nonn,base,easy
%O A297282 1,1
%A A297282 _Clark Kimberling_, Jan 17 2018