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A297256 Numbers whose base-5 digits have equal down-variation and up-variation; see Comments. 4
1, 2, 3, 4, 6, 12, 18, 24, 26, 31, 36, 41, 46, 52, 57, 62, 67, 72, 78, 83, 88, 93, 98, 104, 109, 114, 119, 124, 126, 131, 136, 141, 146, 151, 156, 161, 166, 171, 176, 181, 186, 191, 196, 201, 206, 211, 216, 221, 226, 231, 236, 241, 246, 252, 257, 262, 267 (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

267 in base-5:  2,0,3,2, having DV = 3, UV = 3, so that 267 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 = 5; 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]   (* A297255 *)

Take[Flatten[Position[w, 0]], 120]    (* A297256 *)

Take[Flatten[Position[w, 1]], 120]    (* A297257 *)

CROSSREFS

Cf. A297330, A297255, A297257.

Sequence in context: A048302 A043708 A296697 * A029952 A140494 A048316

Adjacent sequences:  A297253 A297254 A297255 * A297257 A297258 A297259

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling, Jan 15 2018

STATUS

approved

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Last modified September 26 23:42 EDT 2021. Contains 347673 sequences. (Running on oeis4.)