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

Author

Clark Kimberling, Jan 15 2018

Keywords

• nonn
• base
• easy

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.

Examples

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

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A297330, A297261, A297263.

Programs

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 *)