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A297257 Numbers whose base-5 digits have greater up-variation than down-variation; see Comments. 4
7, 8, 9, 13, 14, 19, 27, 28, 29, 32, 33, 34, 37, 38, 39, 42, 43, 44, 47, 48, 49, 53, 54, 58, 59, 63, 64, 68, 69, 73, 74, 79, 84, 89, 94, 99, 127, 128, 129, 132, 133, 134, 137, 138, 139, 142, 143, 144, 147, 148, 149, 152, 153, 154, 157, 158, 159, 162, 163 (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

163 in base-5:  1,1,2,3, having DV = 0, UV = 2, so that 163 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 = 5; 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]   (* A297255 *)

Take[Flatten[Position[w, 0]], 120]    (* A297256 *)

Take[Flatten[Position[w, 1]], 120]    (* A297257 *)

CROSSREFS

Cf. A297330, A297255, A297256.

Sequence in context: A174185 A309152 A170933 * A296698 A297131 A289740

Adjacent sequences:  A297254 A297255 A297256 * A297258 A297259 A297260

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling, Jan 15 2018

STATUS

approved

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Last modified August 1 14:44 EDT 2021. Contains 346393 sequences. (Running on oeis4.)