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A297280 Numbers whose base-13 digits have equal down-variation and up-variation; see Comments.

%I A297280 #8 Jan 23 2018 20:01:57
%S A297280 1,2,3,4,5,6,7,8,9,10,11,12,14,28,42,56,70,84,98,112,126,140,154,168,
%T A297280 170,183,196,209,222,235,248,261,274,287,300,313,326,340,353,366,379,
%U A297280 392,405,418,431,444,457,470,483,496,510,523,536,549,562,575,588
%N A297280 Numbers whose base-13 digits have equal down-variation and up-variation; see Comments.
%C A297280 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 A297280 Differs after the zero from A029958 first for 2211 = 1011_13, which is not a palindrome in base 13 but has DV(2211,13) = UV(2211,13) =1. - _R. J. Mathar_, Jan 23 2018
%H A297280 Clark Kimberling, <a href="/A297280/b297280.txt">Table of n, a(n) for n = 1..10000</a>
%e A297280 588 in base-13:  3,6,3, having DV = 3, UV = 3, so that 588 is in the sequence.
%t A297280 g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
%t A297280 x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
%t A297280 b = 13; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
%t A297280 w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];
%t A297280 Take[Flatten[Position[w, -1]], 120]   (* A297279 *)
%t A297280 Take[Flatten[Position[w, 0]], 120]    (* A297280 *)
%t A297280 Take[Flatten[Position[w, 1]], 120]    (* A297281 *)
%Y A297280 Cf. A297330, A297279, A297281.
%K A297280 nonn,base,easy
%O A297280 1,2
%A A297280 _Clark Kimberling_, Jan 17 2018