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A297281 Numbers whose base-13 digits have greater up-variation than down-variation; see Comments. 4

%I #8 Jan 23 2018 20:06:25

%S 15,16,17,18,19,20,21,22,23,24,25,29,30,31,32,33,34,35,36,37,38,43,44,

%T 45,46,47,48,49,50,51,57,58,59,60,61,62,63,64,71,72,73,74,75,76,77,85,

%U 86,87,88,89,90,99,100,101,102,103,113,114,115,116,127,128

%N Numbers whose base-13 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.

%C Differs from A296751 for example at 171 = 102_13, which is in this sequence because UV(171,13) = 2 > DV(171,13)=1, but not in A296751 because the number of rises and falls are equal. - _R. J. Mathar_, Jan 23 2018

%H Clark Kimberling, <a href="/A297281/b297281.txt">Table of n, a(n) for n = 1..10000</a>

%e 128 in base-13: 9,11, having DV = 0, UV = 2, so that 28 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 = 13; 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] (* A297279 *)

%t Take[Flatten[Position[w, 0]], 120] (* A297280 *)

%t Take[Flatten[Position[w, 1]], 120] (* A297281 *)

%Y Cf. A297330, A297279, A297280.

%K nonn,base,easy

%O 1,1

%A _Clark Kimberling_, Jan 17 2018

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Last modified February 29 10:33 EST 2024. Contains 370418 sequences. (Running on oeis4.)