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A297260 Numbers whose base-6 digits have greater up-variation than down-variation; 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

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

EXAMPLE

136 in base-6:  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

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Last modified February 15 20:32 EST 2019. Contains 320138 sequences. (Running on oeis4.)