A297277 - OEIS

%I #9 Jan 23 2018 19:56:32

%S 1,2,3,4,5,6,7,8,9,10,11,13,26,39,52,65,78,91,104,117,130,143,145,157,

%T 169,181,193,205,217,229,241,253,265,277,290,302,314,326,338,350,362,

%U 374,386,398,410,422,435,447,459,471,483,495,507,519,531,543,555

%N Numbers whose base-12 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 A029957 after the zero for 1741 = 1011_12, which is not a palindrome in base 12 but has DV(1741,12) = UV(1741,12) =1. - _R. J. Mathar_, Jan 23 2018

%H Clark Kimberling, <a href="/A297277/b297277.txt">Table of n, a(n) for n = 1..10000</a>

%e 555 in base-12:  3,10,3, having DV = 7, UV = 7, so that 555 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 = 12; 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]   (* A297276 *)

%t Take[Flatten[Position[w, 0]], 120]    (* A297277 *)

%t Take[Flatten[Position[w, 1]], 120]    (* A297278 *)

%Y Cf. A297330, A297276, A297278.

%K nonn,base,easy

%O 1,2

%A _Clark Kimberling_, Jan 16 2018