A297285 Numbers whose base-15 digits have greater down-variation than up-variation; see Comments.

15, 30, 31, 45, 46, 47, 60, 61, 62, 63, 75, 76, 77, 78, 79, 90, 91, 92, 93, 94, 95, 105, 106, 107, 108, 109, 110, 111, 120, 121, 122, 123, 124, 125, 126, 127, 135, 136, 137, 138, 139, 140, 141, 142, 143, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 165

Offset: 1

Author

Clark Kimberling, Jan 17 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.

Differs from A296758 first for 255 = 120_15, which has the same number of rises and falls and is not in A296758, but DV(255,15) =2 > UV(255,15) =1 and is in this sequence. - R. J. Mathar, Jan 23 2018

Examples

			165 in base-15:  11,0 having DV = 11, UV = 0, so that 165 is in the sequence.
		

Links

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

Crossrefs

Cf. A297330, A297286, A297287.

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 = 15; 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]   (* A297285 *)
Take[Flatten[Position[w, 0]], 120]    (* A297286 *)
Take[Flatten[Position[w, 1]], 120]    (* A297287 *)