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A297255 Numbers whose base-5 digits have greater down-variation than up-variation; see Comments. 4
5, 10, 11, 15, 16, 17, 20, 21, 22, 23, 25, 30, 35, 40, 45, 50, 51, 55, 56, 60, 61, 65, 66, 70, 71, 75, 76, 77, 80, 81, 82, 85, 86, 87, 90, 91, 92, 95, 96, 97, 100, 101, 102, 103, 105, 106, 107, 108, 110, 111, 112, 113, 115, 116, 117, 118, 120, 121, 122, 123 (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

123 in base-5:  4,4,3, having DV = 1, UV = 0, so that 123 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, A297256, A297257.

Sequence in context: A116033 A290469 A140507 * A296699 A297132 A136823

Adjacent sequences:  A297252 A297253 A297254 * A297256 A297257 A297258

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling, Jan 15 2018

STATUS

approved

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Last modified September 16 08:29 EDT 2021. Contains 347469 sequences. (Running on oeis4.)