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A297254 Numbers whose base-4 digits have greater up-variation than down-variation; see Comments. 4
6, 7, 11, 18, 19, 22, 23, 26, 27, 30, 31, 35, 39, 43, 47, 66, 67, 70, 71, 74, 75, 78, 79, 82, 83, 86, 87, 90, 91, 94, 95, 98, 99, 102, 103, 106, 107, 110, 111, 114, 115, 118, 119, 122, 123, 126, 127, 131, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175 (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

175 in base-4:  2,2,3,3, having DV = 0, UV = 1, so that 175 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 = 4; 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]   (* A297252 *)

Take[Flatten[Position[w, 0]], 120]    (* A297253 *)

Take[Flatten[Position[w, 1]], 120]    (* A297254 *)

CROSSREFS

Cf. A297330, A297252, A297253.

Sequence in context: A182156 A166496 A267413 * A347512 A296695 A228948

Adjacent sequences:  A297251 A297252 A297253 * A297255 A297256 A297257

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling, Jan 15 2018

STATUS

approved

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Last modified September 20 17:42 EDT 2021. Contains 347588 sequences. (Running on oeis4.)