A297278 Numbers whose base-12 digits have greater up-variation than down-variation; see Comments.

14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 27, 28, 29, 30, 31, 32, 33, 34, 35, 40, 41, 42, 43, 44, 45, 46, 47, 53, 54, 55, 56, 57, 58, 59, 66, 67, 68, 69, 70, 71, 79, 80, 81, 82, 83, 92, 93, 94, 95, 105, 106, 107, 118, 119, 131, 146, 147, 148, 149, 150, 151

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

151 in base-12:  1,0,7, having DV = 1, UV = 7, so that 151 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 = 12; 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]   (* A297276 *)
Take[Flatten[Position[w, 0]], 120]    (* A297277 *)
Take[Flatten[Position[w, 1]], 120]    (* A297278 *)

Crossrefs

Cf. A297330, A297276, A297277.

Sequence in context: A004455 A142865 A089838 * A296748 A270042 A332924

Adjacent sequences: A297275 A297276 A297277 * A297279 A297280 A297281

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 17 2018

Status

approved