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A297265 Numbers whose base-8 digits have equal down-variation and up-variation; see Comments. 4
1, 2, 3, 4, 5, 6, 7, 9, 18, 27, 36, 45, 54, 63, 65, 73, 81, 89, 97, 105, 113, 121, 130, 138, 146, 154, 162, 170, 178, 186, 195, 203, 211, 219, 227, 235, 243, 251, 260, 268, 276, 284, 292, 300, 308, 316, 325, 333, 341, 349, 357, 365, 373, 381, 390, 398, 406 (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.

a(n) = A029803(n+1) for 1 <= n < 72, but a(72) = 521 differs from A029803(73) = 585. - Georg Fischer, Oct 30 2018

LINKS

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

EXAMPLE

406 in base-8:  6,2,6, having DV = 4, UV = 4, so that 406 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 = 8; 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]   (* A297264 *)

Take[Flatten[Position[w, 0]], 120]    (* A297265 *)

Take[Flatten[Position[w, 1]], 120]    (* A297266 *)

CROSSREFS

Cf. A297330, A297264, A297266.

Sequence in context: A043711 A296706 A029803 * A048319 A037405 A048333

Adjacent sequences:  A297262 A297263 A297264 * A297266 A297267 A297268

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling, Jan 15 2018

STATUS

approved

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Last modified May 26 03:55 EDT 2022. Contains 354074 sequences. (Running on oeis4.)