A297257 Numbers whose base-5 digits have greater up-variation than down-variation; see Comments.

7, 8, 9, 13, 14, 19, 27, 28, 29, 32, 33, 34, 37, 38, 39, 42, 43, 44, 47, 48, 49, 53, 54, 58, 59, 63, 64, 68, 69, 73, 74, 79, 84, 89, 94, 99, 127, 128, 129, 132, 133, 134, 137, 138, 139, 142, 143, 144, 147, 148, 149, 152, 153, 154, 157, 158, 159, 162, 163

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

163 in base-5:  1,1,2,3, having DV = 0, UV = 2, so that 163 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 = 5; 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]   (* A297255 *)
Take[Flatten[Position[w, 0]], 120]    (* A297256 *)
Take[Flatten[Position[w, 1]], 120]    (* A297257 *)

Crossrefs

Cf. A297330, A297255, A297256.

Sequence in context: A174185 A309152 A170933 * A296698 A297131 A289740

Adjacent sequences: A297254 A297255 A297256 * A297258 A297259 A297260

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 15 2018

Status

approved