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A297261 Numbers whose base-7 digits have greater up-variation than down-variation; see Comments. 4
7, 14, 15, 21, 22, 23, 28, 29, 30, 31, 35, 36, 37, 38, 39, 42, 43, 44, 45, 46, 47, 49, 56, 63, 70, 77, 84, 91, 98, 99, 105, 106, 112, 113, 119, 120, 126, 127, 133, 134, 140, 141, 147, 148, 149, 154, 155, 156, 161, 162, 163, 168, 169, 170, 175, 176, 177, 182 (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

182 in base-7:  3,5,0, having DV = 7, UV = 0, so that 182 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 = 7; 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]   (* A297261 *)

Take[Flatten[Position[w, 0]], 120]    (* A297262 *)

Take[Flatten[Position[w, 1]], 120]    (* A297263 *)

CROSSREFS

Cf. A297330, A297262, A297263.

Sequence in context: A107976 A022557 A307546 * A296705 A297138 A085335

Adjacent sequences:  A297258 A297259 A297260 * A297262 A297263 A297264

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling, Jan 15 2018

STATUS

approved

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Last modified June 30 02:41 EDT 2022. Contains 354913 sequences. (Running on oeis4.)