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A297252 Numbers whose base-4 digits have greater down-variation than up-variation; see Comments. 4
4, 8, 9, 12, 13, 14, 16, 20, 24, 28, 32, 33, 36, 37, 40, 41, 44, 45, 48, 49, 50, 52, 53, 54, 56, 57, 58, 60, 61, 62, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 129, 132, 133, 136, 137, 140, 141, 144, 145, 148, 149, 152, 153 (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

153 in base-4:  2,1,2,1, having DV = 2, UV = 1, so that 153 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, A297253, A297254.

Sequence in context: A229004 A306976 A266142 * A296696 A297129 A078137

Adjacent sequences:  A297249 A297250 A297251 * A297253 A297254 A297255

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling, Jan 15 2018

STATUS

approved

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Last modified June 26 04:11 EDT 2019. Contains 324369 sequences. (Running on oeis4.)