A297276 Numbers whose base-12 digits have greater down-variation than up-variation; see Comments.

12, 24, 25, 36, 37, 38, 48, 49, 50, 51, 60, 61, 62, 63, 64, 72, 73, 74, 75, 76, 77, 84, 85, 86, 87, 88, 89, 90, 96, 97, 98, 99, 100, 101, 102, 103, 108, 109, 110, 111, 112, 113, 114, 115, 116, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 132, 133, 134

Offset: 1

Author

Clark Kimberling, Jan 16 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 A296749 first at 168 = 120_12, which is in not in A296749 because it has the same number of rises and falls, but in here because DV(168,12) =2 > UV(168,12) =1. - R. J. Mathar, Jan 23 2018

Examples

			134 in base-12:  11,2, having DV = 9, UV = 0, so that 134 is in the sequence.
		

Links

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

Crossrefs

Cf. A297330, A297277, A297278.

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 = 12; 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]   (* A297276 *)
Take[Flatten[Position[w, 0]], 120]    (* A297277 *)
Take[Flatten[Position[w, 1]], 120]    (* A297278 *)