

A297260


Numbers whose base6 digits have greater upvariation than downvariation; see Comments.


4



8, 9, 10, 11, 15, 16, 17, 22, 23, 29, 38, 39, 40, 41, 44, 45, 46, 47, 50, 51, 52, 53, 56, 57, 58, 59, 62, 63, 64, 65, 68, 69, 70, 71, 75, 76, 77, 81, 82, 83, 87, 88, 89, 93, 94, 95, 99, 100, 101, 105, 106, 107, 112, 113, 118, 119, 124, 125, 130, 131, 136
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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

136 in base6: 3,4,4, having DV = 0, UV = 1, so that 136 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 = 6; 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] (* A297258 *)
Take[Flatten[Position[w, 0]], 120] (* A297259 *)
Take[Flatten[Position[w, 1]], 120] (* A297260 *)


CROSSREFS

Cf. A297330, A297258, A297259.
Sequence in context: A058366 A120209 A247631 * A296701 A297134 A247455
Adjacent sequences: A297257 A297258 A297259 * A297261 A297262 A297263


KEYWORD

nonn,base,easy


AUTHOR

Clark Kimberling, Jan 15 2018


STATUS

approved



