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A297251 Numbers whose base-3 digits have greater up-variation than down-variation; see Comments. 4
5, 11, 14, 17, 29, 32, 35, 38, 41, 44, 47, 50, 53, 83, 86, 89, 92, 95, 98, 101, 104, 107, 110, 113, 116, 119, 122, 125, 128, 131, 134, 137, 140, 143, 146, 149, 152, 155, 158, 161, 245, 248, 251, 254, 257, 260, 263, 266, 269, 272, 275, 278, 281, 284, 287, 290 (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

290 in base-3:  1,0,1,2,0,2, having DV = 3, UV = 4, so that 147 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 = 3; 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]   (* A297249 *)

Take[Flatten[Position[w, 0]], 120]    (* A297250 *)

Take[Flatten[Position[w, 1]], 120]    (* A297251 *)

CROSSREFS

Cf. A297249, A297250, A297330.

Sequence in context: A275640 A275805 A313993 * A293834 A313994 A228706

Adjacent sequences:  A297248 A297249 A297250 * A297252 A297253 A297254

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling, Apr 10 2018

STATUS

approved

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Last modified June 17 04:26 EDT 2019. Contains 324183 sequences. (Running on oeis4.)