A297288 Numbers whose base-16 digits have greater down-variation than up-variation; see Comments.

16, 32, 33, 48, 49, 50, 64, 65, 66, 67, 80, 81, 82, 83, 84, 96, 97, 98, 99, 100, 101, 112, 113, 114, 115, 116, 117, 118, 128, 129, 130, 131, 132, 133, 134, 135, 144, 145, 146, 147, 148, 149, 150, 151, 152, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169

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 A296761 first at 288 = 120_16, which has the same number of rises and falls (so not in A296761) but DV =2 > UV =1 (so in this sequence). - R. J. Mathar, Jan 23 2018

Links

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

Example

169 in base-16:  10,9 having DV = 1, UV = 0, so that 169 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 = 16; 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]   (* A297288 *)
Take[Flatten[Position[w, 0]], 120]    (* A297289 *)
Take[Flatten[Position[w, 1]], 120]    (* A297290 *)

Crossrefs

Cf. A297330, A297289, A297290.

Sequence in context: A059164 A040240 A296761 * A335246 A055075 A359831

Adjacent sequences: A297285 A297286 A297287 * A297289 A297290 A297291

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 17 2018

Status

approved