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A297280 Numbers whose base-13 digits have equal down-variation and up-variation; see Comments. 4
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 170, 183, 196, 209, 222, 235, 248, 261, 274, 287, 300, 313, 326, 340, 353, 366, 379, 392, 405, 418, 431, 444, 457, 470, 483, 496, 510, 523, 536, 549, 562, 575, 588 (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 after the zero from A029958 first for 2211 = 1011_13, which is not a palindrome in base 13 but has DV(2211,13) = UV(2211,13) =1. - R. J. Mathar, Jan 23 2018

LINKS

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

EXAMPLE

588 in base-13:  3,6,3, having DV = 3, UV = 3, so that 588 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 = 13; 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]   (* A297279 *)

Take[Flatten[Position[w, 0]], 120]    (* A297280 *)

Take[Flatten[Position[w, 1]], 120]    (* A297281 *)

CROSSREFS

Cf. A297330, A297279, A297281.

Sequence in context: A043716 A296750 A029958 * A048324 A048337 A003964

Adjacent sequences:  A297277 A297278 A297279 * A297281 A297282 A297283

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling, Jan 17 2018

STATUS

approved

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Last modified June 15 00:00 EDT 2021. Contains 345041 sequences. (Running on oeis4.)