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A297258 Numbers whose base-6 digits have greater down-variation than up-variation; see Comments. 4
6, 12, 13, 18, 19, 20, 24, 25, 26, 27, 30, 31, 32, 33, 34, 36, 42, 48, 54, 60, 66, 72, 73, 78, 79, 84, 85, 90, 91, 96, 97, 102, 103, 108, 109, 110, 114, 115, 116, 120, 121, 122, 126, 127, 128, 132, 133, 134, 138, 139, 140, 144, 145, 146, 147, 150, 151, 152 (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

152 in base-6:  4,1,2, having DV = 3, UV = 1, so that 152 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 = 6; 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]   (* A297258 *)

Take[Flatten[Position[w, 0]], 120]    (* A297259 *)

Take[Flatten[Position[w, 1]], 120]    (* A297260 *)

CROSSREFS

Cf. A297330, A297259, A297260.

Sequence in context: A004749 A107687 A337480 * A296702 A297135 A004758

Adjacent sequences:  A297255 A297256 A297257 * A297259 A297260 A297261

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling, Jan 15 2018

STATUS

approved

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Last modified September 23 15:23 EDT 2021. Contains 347618 sequences. (Running on oeis4.)