A297266 Numbers whose base-8 digits have greater up-variation than down-variation; see Comments.

10, 11, 12, 13, 14, 15, 19, 20, 21, 22, 23, 28, 29, 30, 31, 37, 38, 39, 46, 47, 55, 66, 67, 68, 69, 70, 71, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 98, 99, 100, 101, 102, 103, 106, 107, 108, 109, 110, 111, 114, 115, 116, 117

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

111 in base-8:  1,5,7, having DV = 0, UV = 6, so that 111 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, A297265.

Sequence in context: A058946 A118379 A174397 * A296707 A297140 A173688

Adjacent sequences: A297263 A297264 A297265 * A297267 A297268 A297269

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 15 2018

Status

approved