A297275 Numbers whose base-11 digits have greater up-variation than down-variation; see Comments.

13, 14, 15, 16, 17, 18, 19, 20, 21, 25, 26, 27, 28, 29, 30, 31, 32, 37, 38, 39, 40, 41, 42, 43, 49, 50, 51, 52, 53, 54, 61, 62, 63, 64, 65, 73, 74, 75, 76, 85, 86, 87, 97, 98, 109, 123, 124, 125, 126, 127, 128, 129, 130, 131, 134, 135, 136, 137, 138, 139

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

139 in base-11:  1,1,7, having DV = 0, UV = 6, so that 139 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 = 11; 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]   (* A297273 *)
Take[Flatten[Position[w, 0]], 120]    (* A297274 *)
Take[Flatten[Position[w, 1]], 120]    (* A297275 *)

Crossrefs

Cf. A297330, A297273, A297274.

Sequence in context: A004502 A020512 A337159 * A296745 A178402 A132580

Adjacent sequences: A297272 A297273 A297274 * A297276 A297277 A297278

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 16 2018

Status

approved