A297269 Numbers whose base-9 digits have greater up-variation than down-variation; see Comments.

11, 12, 13, 14, 15, 16, 17, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 41, 42, 43, 44, 51, 52, 53, 61, 62, 71, 83, 84, 85, 86, 87, 88, 89, 92, 93, 94, 95, 96, 97, 98, 101, 102, 103, 104, 105, 106, 107, 110, 111, 112, 113, 114, 115, 116, 119, 120, 121, 122

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

122 in base-9:  1,4,5, having DV = 0, UV = 4, so that 122 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, A297268.

Sequence in context: A162672 A110403 A119247 * A296710 A297143 A138595

Adjacent sequences: A297266 A297267 A297268 * A297270 A297271 A297272

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 15 2018

Status

approved