A297263 Numbers whose base-7 digits have greater up-variation than down-variation; see Comments.

9, 10, 11, 12, 13, 17, 18, 19, 20, 25, 26, 27, 33, 34, 41, 51, 52, 53, 54, 55, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 79, 80, 81, 82, 83, 86, 87, 88, 89, 90, 93, 94, 95, 96, 97, 101, 102, 103, 104, 108, 109, 110, 111, 115, 116, 117, 118

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

118 in base-7:  2,2,6, having DV = 0, UV = 4, so that 118 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 = 7; 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]   (* A297261 *)
Take[Flatten[Position[w, 0]], 120]    (* A297262 *)
Take[Flatten[Position[w, 1]], 120]    (* A297263 *)

Crossrefs

Cf. A297330, A297261, A297262.

Sequence in context: A281196 A001731 A268360 * A296704 A297137 A129849

Adjacent sequences: A297260 A297261 A297262 * A297264 A297265 A297266

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 15 2018

Status

approved