

A297279


Numbers whose base13 digits have greater downvariation than upvariation; see Comments.


4



13, 26, 27, 39, 40, 41, 52, 53, 54, 55, 65, 66, 67, 68, 69, 78, 79, 80, 81, 82, 83, 91, 92, 93, 94, 95, 96, 97, 104, 105, 106, 107, 108, 109, 110, 111, 117, 118, 119, 120, 121, 122, 123, 124, 125, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 143, 144
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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 A296752 first for 195 = 120_13, which has the same number of rises and falls and is therefore not in A296752, but has DV(195,13) =2 > UV(195,13) = 1 and is in this sequence.  R. J. Mathar, Jan 23 2018


LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000


EXAMPLE

144 in base13: 11,1, having DV = 10, UV = 0, so that 144 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 = 13; 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] (* A297279 *)
Take[Flatten[Position[w, 0]], 120] (* A297280 *)
Take[Flatten[Position[w, 1]], 120] (* A297281 *)


CROSSREFS

Cf. A297330, A297280, A297281.
Sequence in context: A238338 A040156 A296752 * A095781 A037974 A318957
Adjacent sequences: A297276 A297277 A297278 * A297280 A297281 A297282


KEYWORD

nonn,base,easy


AUTHOR

Clark Kimberling, Jan 17 2018


STATUS

approved



