A297287 Numbers whose base-15 digits have greater up-variation than down-variation; see Comments.

17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 81, 82, 83, 84, 85, 86, 87, 88, 89, 97, 98, 99, 100, 101, 102, 103, 104

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 A296757 first for 227 = 102_15, which has UV= 2 > DV=1 and is in this sequence, but has the same number of rises and falls (so not in A296757). - R. J. Mathar, Jan 23 2018

Links

Table of n, a(n) for n=1..63.

Example

104 in base-15:  6,14 having DV = 0, UV = 8, so that 104 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 = 15; 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]   (* A297285 *)
Take[Flatten[Position[w, 0]], 120]    (* A297286 *)
Take[Flatten[Position[w, 1]], 120]    (* A297287 *)

Crossrefs

Cf. A297330, A297285, A297286.

Sequence in context: A165838 A217543 A296757 * A018822 A304488 A043594

Adjacent sequences: A297284 A297285 A297286 * A297288 A297289 A297290

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 17 2018

Status

approved