A297254 Numbers whose base-4 digits have greater up-variation than down-variation; see Comments.

6, 7, 11, 18, 19, 22, 23, 26, 27, 30, 31, 35, 39, 43, 47, 66, 67, 70, 71, 74, 75, 78, 79, 82, 83, 86, 87, 90, 91, 94, 95, 98, 99, 102, 103, 106, 107, 110, 111, 114, 115, 118, 119, 122, 123, 126, 127, 131, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175

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

175 in base-4:  2,2,3,3, having DV = 0, UV = 1, so that 175 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 = 4; 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]   (* A297252 *)
Take[Flatten[Position[w, 0]], 120]    (* A297253 *)
Take[Flatten[Position[w, 1]], 120]    (* A297254 *)

Crossrefs

Cf. A297330, A297252, A297253.

Sequence in context: A182156 A166496 A267413 * A347512 A296695 A228948

Adjacent sequences: A297251 A297252 A297253 * A297255 A297256 A297257

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 15 2018

Status

approved