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A297269 Numbers whose base-9 digits have greater up-variation than down-variation; see Comments. 4
11, 12, 13, 14, 15, 16, 17, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 41, 42, 43, 44, 51, 52, 53, 61, 62, 71, 83, 84, 85, 86, 87, 88, 89, 92, 93, 94, 95, 96, 97, 98, 101, 102, 103, 104, 105, 106, 107, 110, 111, 112, 113, 114, 115, 116, 119, 120, 121, 122 (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

122 in base-9:  1,4,5, having DV = 0, UV = 4, so that 122 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 = 9; 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]   (* A297267 *)

Take[Flatten[Position[w, 0]], 120]    (* A297268 *)

Take[Flatten[Position[w, 1]], 120]    (* A297269 *)

CROSSREFS

Cf. A297330, A297267, A297268.

Sequence in context: A162672 A110403 A119247 * A296710 A297143 A138595

Adjacent sequences:  A297266 A297267 A297268 * A297270 A297271 A297272

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling, Jan 15 2018

STATUS

approved

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Last modified December 7 00:16 EST 2019. Contains 329812 sequences. (Running on oeis4.)