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A297281 Numbers whose base-13 digits have greater up-variation than down-variation; see Comments. 4
15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 43, 44, 45, 46, 47, 48, 49, 50, 51, 57, 58, 59, 60, 61, 62, 63, 64, 71, 72, 73, 74, 75, 76, 77, 85, 86, 87, 88, 89, 90, 99, 100, 101, 102, 103, 113, 114, 115, 116, 127, 128 (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.

Differs from A296751 for example at 171 = 102_13, which is in this sequence because UV(171,13) = 2 > DV(171,13)=1, but not in A296751 because the number of rises and falls are equal. - R. J. Mathar, Jan 23 2018

LINKS

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

EXAMPLE

128 in base-13:  9,11, having DV = 0, UV = 2, so that 28 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, A297279, A297280.

Sequence in context: A291575 A004504 A296751 * A176294 A214424 A090461

Adjacent sequences:  A297278 A297279 A297280 * A297282 A297283 A297284

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling, Jan 17 2018

STATUS

approved

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Last modified October 22 10:39 EDT 2021. Contains 348160 sequences. (Running on oeis4.)