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A297279 Numbers whose base-13 digits have greater down-variation than up-variation; see Comments. 4
13, 26, 27, 39, 40, 41, 52, 53, 54, 55, 65, 66, 67, 68, 69, 78, 79, 80, 81, 82, 83, 91, 92, 93, 94, 95, 96, 97, 104, 105, 106, 107, 108, 109, 110, 111, 117, 118, 119, 120, 121, 122, 123, 124, 125, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 143, 144 (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 A296752 first for 195 = 120_13, which has the same number of rises and falls and is therefore not in A296752, but has DV(195,13) =2 > UV(195,13) = 1 and is in this sequence. - R. J. Mathar, Jan 23 2018

LINKS

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

EXAMPLE

144 in base-13:  11,1, having DV = 10, UV = 0, so that 144 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 = 13; 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]   (* A297279 *)

Take[Flatten[Position[w, 0]], 120]    (* A297280 *)

Take[Flatten[Position[w, 1]], 120]    (* A297281 *)

CROSSREFS

Cf. A297330, A297280, A297281.

Sequence in context: A238338 A040156 A296752 * A095781 A037974 A318957

Adjacent sequences:  A297276 A297277 A297278 * A297280 A297281 A297282

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling, Jan 17 2018

STATUS

approved

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Last modified September 18 18:15 EDT 2019. Contains 327178 sequences. (Running on oeis4.)