A297260 Numbers whose base-6 digits have greater up-variation than down-variation; see Comments.

8, 9, 10, 11, 15, 16, 17, 22, 23, 29, 38, 39, 40, 41, 44, 45, 46, 47, 50, 51, 52, 53, 56, 57, 58, 59, 62, 63, 64, 65, 68, 69, 70, 71, 75, 76, 77, 81, 82, 83, 87, 88, 89, 93, 94, 95, 99, 100, 101, 105, 106, 107, 112, 113, 118, 119, 124, 125, 130, 131, 136

Offset

1,1

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

136 in base-6:  3,4,4, having DV = 0, UV = 1, so that 136 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 = 6; 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]   (* A297258 *)
Take[Flatten[Position[w, 0]], 120]    (* A297259 *)
Take[Flatten[Position[w, 1]], 120]    (* A297260 *)

Crossrefs

Cf. A297330, A297258, A297259.

Sequence in context: A058366 A120209 A247631 * A296701 A297134 A247455

Adjacent sequences: A297257 A297258 A297259 * A297261 A297262 A297263

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 15 2018

Status

approved