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A297276 Numbers whose base-12 digits have greater down-variation than up-variation; see Comments. 4
12, 24, 25, 36, 37, 38, 48, 49, 50, 51, 60, 61, 62, 63, 64, 72, 73, 74, 75, 76, 77, 84, 85, 86, 87, 88, 89, 90, 96, 97, 98, 99, 100, 101, 102, 103, 108, 109, 110, 111, 112, 113, 114, 115, 116, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 132, 133, 134 (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.

Differs from A296749 first at 168 = 120_12, which is in not in A296749 because it has the same number of rises and falls, but in here because DV(168,12) =2 > UV(168,12) =1. - R. J. Mathar, Jan 23 2018

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000

EXAMPLE

134 in base-12:  11,2, having DV = 9, UV = 0, so that 134 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 = 12; 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]   (* A297276 *)

Take[Flatten[Position[w, 0]], 120]    (* A297277 *)

Take[Flatten[Position[w, 1]], 120]    (* A297278 *)

CROSSREFS

Cf. A297330, A297277, A297278.

Sequence in context: A117320 A040132 A296749 * A095780 A119588 A167994

Adjacent sequences:  A297273 A297274 A297275 * A297277 A297278 A297279

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling, Jan 16 2018

STATUS

approved

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Last modified August 1 17:38 EDT 2021. Contains 346402 sequences. (Running on oeis4.)