cp's OEIS Frontend

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

%I A297257 #4 Jan 15 2018 21:08:12
%S A297257 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 A297257 59,63,64,68,69,73,74,79,84,89,94,99,127,128,129,132,133,134,137,138,
%U A297257 139,142,143,144,147,148,149,152,153,154,157,158,159,162,163
%N A297257 Numbers whose base-5 digits have greater up-variation than down-variation; see Comments.
%C A297257 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 A297257 Clark Kimberling, <a href="/A297257/b297257.txt">Table of n, a(n) for n = 1..10000</a>
%e A297257 163 in base-5:  1,1,2,3, having DV = 0, UV = 2, so that 163 is in the sequence.
%t A297257 g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
%t A297257 x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
%t A297257 b = 5; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
%t A297257 w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];
%t A297257 Take[Flatten[Position[w, -1]], 120]   (* A297255 *)
%t A297257 Take[Flatten[Position[w, 0]], 120]    (* A297256 *)
%t A297257 Take[Flatten[Position[w, 1]], 120]    (* A297257 *)
%Y A297257 Cf. A297330, A297255, A297256.
%K A297257 nonn,base,easy
%O A297257 1,1
%A A297257 _Clark Kimberling_, Jan 15 2018