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A297262 Numbers whose base-7 digits have equal up-variation and down-variation; see Comments. 4
1, 2, 3, 4, 5, 6, 8, 16, 24, 32, 40, 48, 50, 57, 64, 71, 78, 85, 92, 100, 107, 114, 121, 128, 135, 142, 150, 157, 164, 171, 178, 185, 192, 200, 207, 214, 221, 228, 235, 242, 250, 257, 264, 271, 278, 285, 292, 300, 307, 314, 321, 328, 335, 342, 344, 351, 358 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

358 in base-7:  1,0,2,1, having DV = 2, UV = 2, so that 358 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, A297261, A297263.

Sequence in context: A048304 A043710 A296703 * A029954 A048318 A037402

Adjacent sequences:  A297259 A297260 A297261 * A297263 A297264 A297265

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling, Jan 15 2018

STATUS

approved

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Last modified July 7 05:42 EDT 2022. Contains 355141 sequences. (Running on oeis4.)