A297264 Numbers whose base-8 digits have greater down-variation than up-variation; see Comments.

8, 16, 17, 24, 25, 26, 32, 33, 34, 35, 40, 41, 42, 43, 44, 48, 49, 50, 51, 52, 53, 56, 57, 58, 59, 60, 61, 62, 64, 72, 80, 88, 96, 104, 112, 120, 128, 129, 136, 137, 144, 145, 152, 153, 160, 161, 168, 169, 176, 177, 184, 185, 192, 193, 194, 200, 201, 202

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

202 in base-8:  3,1,2, having DV = 2, UV = 1, so that 202 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 = 8; 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]   (* A297264 *)
Take[Flatten[Position[w, 0]], 120]    (* A297265 *)
Take[Flatten[Position[w, 1]], 120]    (* A297266 *)

Crossrefs

Cf. A297330, A297265, A297266.

Sequence in context: A363982 A319317 A091251 * A296708 A297141 A004779

Adjacent sequences: A297261 A297262 A297263 * A297265 A297266 A297267

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 15 2018

Status

approved