

A297276


Numbers whose base12 digits have greater downvariation than upvariation; see Comments.


4



12, 24, 25, 36, 37, 38, 48, 49, 50, 51, 60, 61, 62, 63, 64, 72, 73, 74, 75, 76, 77, 84, 85, 86, 87, 88, 89, 90, 96, 97, 98, 99, 100, 101, 102, 103, 108, 109, 110, 111, 112, 113, 114, 115, 116, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 132, 133, 134
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OFFSET

1,1


COMMENTS

Suppose that n has baseb digits b(m), b(m1), ..., b(0). The baseb downvariation of n is the sum DV(n,b) of all d(i)d(i1) for which d(i) > d(i1); the baseb upvariation of n is the sum UV(n,b) of all d(k1)d(k) for which d(k) < d(k1). The total baseb variation of n is the sum TV(n,b) = DV(n,b) + UV(n,b). See the guide at A297330.
Differs from A296749 first at 168 = 120_12, which is in not in A296749 because it has the same number of rises and falls, but in here because DV(168,12) =2 > UV(168,12) =1.  R. J. Mathar, Jan 23 2018


LINKS



EXAMPLE

134 in base12: 11,2, having DV = 9, UV = 0, so that 134 is in the sequence.


MATHEMATICA

g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
b = 12; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
w = Sign[Flatten[p /. {} > {0}] + Flatten[q /. {} > {0}]];
Take[Flatten[Position[w, 1]], 120] (* A297276 *)
Take[Flatten[Position[w, 0]], 120] (* A297277 *)
Take[Flatten[Position[w, 1]], 120] (* A297278 *)


CROSSREFS



KEYWORD

nonn,base,easy


AUTHOR



STATUS

approved



