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

1,1

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.

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

Links

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

Example

165 in base-15:  11,0 having DV = 11, UV = 0, so that 165 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 = 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 *)

Crossrefs

Cf. A297330, A297286, A297287.

Sequence in context: A322370 A040210 A296758 * A115776 A095783 A348556

Adjacent sequences: A297282 A297283 A297284 * A297286 A297287 A297288

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 17 2018

Status

approved