A297262 Numbers whose base-7 digits have equal up-variation and down-variation; see Comments.

1, 2, 3, 4, 5, 6, 8, 16, 24, 32, 40, 48, 50, 57, 64, 71, 78, 85, 92, 100, 107, 114, 121, 128, 135, 142, 150, 157, 164, 171, 178, 185, 192, 200, 207, 214, 221, 228, 235, 242, 250, 257, 264, 271, 278, 285, 292, 300, 307, 314, 321, 328, 335, 342, 344, 351, 358

Offset

1,2

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

358 in base-7:  1,0,2,1, having DV = 2, UV = 2, so that 358 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, A297263.

Sequence in context: A048304 A043710 A296703 * A029954 A048318 A037402

Adjacent sequences: A297259 A297260 A297261 * A297263 A297264 A297265

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 15 2018

Status

approved