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A297268 Numbers whose base-9 digits have equal down-variation and up-variation; see Comments. 4
1, 2, 3, 4, 5, 6, 7, 8, 10, 20, 30, 40, 50, 60, 70, 80, 82, 91, 100, 109, 118, 127, 136, 145, 154, 164, 173, 182, 191, 200, 209, 218, 227, 236, 246, 255, 264, 273, 282, 291, 300, 309, 318, 328, 337, 346, 355, 364, 373, 382, 391, 400, 410, 419, 428, 437, 446 (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.

Differs from A029955 first at 739=1011_9 which is not a palindrome in base 9 but has DV(739,9)=UV(793,9) =1. - R. J. Mathar, Jan 23 2018

LINKS

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

EXAMPLE

446 in base-9:  5,4,5, having DV = 1, UV = 1, so that 446 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 = 9; 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]   (* A297267 *)

Take[Flatten[Position[w, 0]], 120]    (* A297268 *)

Take[Flatten[Position[w, 1]], 120]    (* A297269 *)

CROSSREFS

Cf. A297330, A297267, A297269.

Sequence in context: A043712 A296709 A029955 * A048320 A037407 A048334

Adjacent sequences:  A297265 A297266 A297267 * A297269 A297270 A297271

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling, Jan 15 2018

STATUS

approved

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Last modified November 17 16:05 EST 2019. Contains 329238 sequences. (Running on oeis4.)