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A297275 Numbers whose base-11 digits have greater up-variation than down-variation; see Comments. 4
13, 14, 15, 16, 17, 18, 19, 20, 21, 25, 26, 27, 28, 29, 30, 31, 32, 37, 38, 39, 40, 41, 42, 43, 49, 50, 51, 52, 53, 54, 61, 62, 63, 64, 65, 73, 74, 75, 76, 85, 86, 87, 97, 98, 109, 123, 124, 125, 126, 127, 128, 129, 130, 131, 134, 135, 136, 137, 138, 139 (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

139 in base-11:  1,1,7, having DV = 0, UV = 6, so that 139 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 = 11; 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]   (* A297273 *)

Take[Flatten[Position[w, 0]], 120]    (* A297274 *)

Take[Flatten[Position[w, 1]], 120]    (* A297275 *)

CROSSREFS

Cf. A297330, A297273, A297274.

Sequence in context: A004502 A020512 A337159 * A296745 A178402 A132580

Adjacent sequences:  A297272 A297273 A297274 * A297276 A297277 A297278

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling, Jan 16 2018

STATUS

approved

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Last modified September 17 03:42 EDT 2021. Contains 347478 sequences. (Running on oeis4.)