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A297257 Numbers whose base-5 digits have greater up-variation than down-variation; see Comments. 4

%I

%S 7,8,9,13,14,19,27,28,29,32,33,34,37,38,39,42,43,44,47,48,49,53,54,58,

%T 59,63,64,68,69,73,74,79,84,89,94,99,127,128,129,132,133,134,137,138,

%U 139,142,143,144,147,148,149,152,153,154,157,158,159,162,163

%N Numbers whose base-5 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="/A297257/b297257.txt">Table of n, a(n) for n = 1..10000</a>

%e 163 in base-5: 1,1,2,3, having DV = 0, UV = 2, so that 163 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 = 5; 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] (* A297255 *)

%t Take[Flatten[Position[w, 0]], 120] (* A297256 *)

%t Take[Flatten[Position[w, 1]], 120] (* A297257 *)

%Y Cf. A297330, A297255, A297256.

%K nonn,base,easy

%O 1,1

%A _Clark Kimberling_, Jan 15 2018

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Last modified September 17 09:42 EDT 2021. Contains 347478 sequences. (Running on oeis4.)