A297284 Numbers whose base-14 digits have greater up-variation than down-variation; see Comments.

16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 61, 62, 63, 64, 65, 66, 67, 68, 69, 76, 77, 78, 79, 80, 81, 82, 83, 91, 92, 93, 94, 95, 96, 97, 106, 107, 108, 109, 110, 111

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.

Differs from A296754 first at 198 =102_14, which is in this sequence because UV(102,14) = 2 > DV(102,14) =1, but has the same number of rises and falls and is not in A296754. - R. J. Mathar, Jan 23 2018

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

Example

111 in base-14:  7,13 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 = 14; 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]   (* A297282 *)
Take[Flatten[Position[w, 0]], 120]    (* A297283 *)
Take[Flatten[Position[w, 1]], 120]    (* A297284 *)

Crossrefs

Cf. A297330, A297282, A297283.

Sequence in context: A115420 A250038 A296754 * A270043 A209726 A326455

Adjacent sequences: A297281 A297282 A297283 * A297285 A297286 A297287

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 17 2018

Status

approved