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A297268 Numbers whose base-9 digits have equal down-variation and up-variation; see Comments. 4

%I

%S 1,2,3,4,5,6,7,8,10,20,30,40,50,60,70,80,82,91,100,109,118,127,136,

%T 145,154,164,173,182,191,200,209,218,227,236,246,255,264,273,282,291,

%U 300,309,318,328,337,346,355,364,373,382,391,400,410,419,428,437,446

%N Numbers whose base-9 digits have equal down-variation and up-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 A029955 first at 739=1011_9 which is not a palindrome in base 9 but has DV(739,9)=UV(793,9) =1. - _R. J. Mathar_, Jan 23 2018

%H Clark Kimberling, <a href="/A297268/b297268.txt">Table of n, a(n) for n = 1..10000</a>

%e 446 in base-9: 5,4,5, having DV = 1, UV = 1, so that 446 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 = 9; 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] (* A297267 *)

%t Take[Flatten[Position[w, 0]], 120] (* A297268 *)

%t Take[Flatten[Position[w, 1]], 120] (* A297269 *)

%Y Cf. A297330, A297267, A297269.

%K nonn,base,easy

%O 1,2

%A _Clark Kimberling_, Jan 15 2018

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Last modified December 6 16:24 EST 2019. Contains 329808 sequences. (Running on oeis4.)