A297283 - OEIS

%I #8 Jan 23 2018 20:11:23

%S 1,2,3,4,5,6,7,8,9,10,11,12,13,15,30,45,60,75,90,105,120,135,150,165,

%T 180,195,197,211,225,239,253,267,281,295,309,323,337,351,365,379,394,

%U 408,422,436,450,464,478,492,506,520,534,548,562,576,591,605,619

%N Numbers whose base-14 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 first from A029959 after the zero for 2759 = 1011_14, which is not a palindrome in base 14 but has UV(2759,14) = DV(2759,14) = 1. - _R. J. Mathar_, Jan 23 2018

%H Clark Kimberling, <a href="/A297283/b297283.txt">Table of n, a(n) for n = 1..10000</a>

%e 619 in base-14:  3,2,3 having DV = 1, UV = 1, so that 619 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 = 14; 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]   (* A297282 *)

%t Take[Flatten[Position[w, 0]], 120]    (* A297283 *)

%t Take[Flatten[Position[w, 1]], 120]    (* A297284 *)

%Y Cf. A297330, A297282, A297284.

%K nonn,base,easy

%O 1,2

%A _Clark Kimberling_, Jan 17 2018