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A297278 Numbers whose base-12 digits have greater up-variation than down-variation; see Comments. 4

%I

%S 14,15,16,17,18,19,20,21,22,23,27,28,29,30,31,32,33,34,35,40,41,42,43,

%T 44,45,46,47,53,54,55,56,57,58,59,66,67,68,69,70,71,79,80,81,82,83,92,

%U 93,94,95,105,106,107,118,119,131,146,147,148,149,150,151

%N Numbers whose base-12 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="/A297278/b297278.txt">Table of n, a(n) for n = 1..10000</a>

%e 151 in base-12: 1,0,7, having DV = 1, UV = 7, so that 151 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 = 12; 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] (* A297276 *)

%t Take[Flatten[Position[w, 0]], 120] (* A297277 *)

%t Take[Flatten[Position[w, 1]], 120] (* A297278 *)

%Y Cf. A297330, A297276, A297277.

%K nonn,base,easy

%O 1,1

%A _Clark Kimberling_, Jan 17 2018

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Last modified October 25 09:51 EDT 2021. Contains 348239 sequences. (Running on oeis4.)