

A297278


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


4



14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 27, 28, 29, 30, 31, 32, 33, 34, 35, 40, 41, 42, 43, 44, 45, 46, 47, 53, 54, 55, 56, 57, 58, 59, 66, 67, 68, 69, 70, 71, 79, 80, 81, 82, 83, 92, 93, 94, 95, 105, 106, 107, 118, 119, 131, 146, 147, 148, 149, 150, 151
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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.


LINKS

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


EXAMPLE

151 in base12: 1,0,7, having DV = 1, UV = 7, so that 151 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

Cf. A297330, A297276, A297277.
Sequence in context: A004455 A142865 A089838 * A296748 A270042 A332924
Adjacent sequences: A297275 A297276 A297277 * A297279 A297280 A297281


KEYWORD

nonn,base,easy


AUTHOR

Clark Kimberling, Jan 17 2018


STATUS

approved



