A297279 Numbers whose base-13 digits have greater down-variation than up-variation; see Comments.

13, 26, 27, 39, 40, 41, 52, 53, 54, 55, 65, 66, 67, 68, 69, 78, 79, 80, 81, 82, 83, 91, 92, 93, 94, 95, 96, 97, 104, 105, 106, 107, 108, 109, 110, 111, 117, 118, 119, 120, 121, 122, 123, 124, 125, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 143, 144

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 A296752 first for 195 = 120_13, which has the same number of rises and falls and is therefore not in A296752, but has DV(195,13) =2 > UV(195,13) = 1 and is in this sequence. - R. J. Mathar, Jan 23 2018

Links

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

Example

144 in base-13:  11,1, having DV = 10, UV = 0, so that 144 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 = 13; 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]   (* A297279 *)
Take[Flatten[Position[w, 0]], 120]    (* A297280 *)
Take[Flatten[Position[w, 1]], 120]    (* A297281 *)

Crossrefs

Cf. A297330, A297280, A297281.

Sequence in context: A238338 A040156 A296752 * A095781 A037974 A318957

Adjacent sequences: A297276 A297277 A297278 * A297280 A297281 A297282

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 17 2018

Status

approved