A297282 Numbers whose base-14 digits have greater down-variation than up-variation; see Comments.

14, 28, 29, 42, 43, 44, 56, 57, 58, 59, 70, 71, 72, 73, 74, 84, 85, 86, 87, 88, 89, 98, 99, 100, 101, 102, 103, 104, 112, 113, 114, 115, 116, 117, 118, 119, 126, 127, 128, 129, 130, 131, 132, 133, 134, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 154

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 A296755 first for 224 = 120_14, which is in this sequence because DV(224,14) = 2 > UV(224,14)=1, but not in A296755 because the number of rises equals the number of falls. - R. J. Mathar, Jan 23 2018

Links

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

Example

154 in base-14:  11,0 having DV = 9, UV = 0, so that 154 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 = 14; 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]   (* A297282 *)
Take[Flatten[Position[w, 0]], 120]    (* A297283 *)
Take[Flatten[Position[w, 1]], 120]    (* A297284 *)

Crossrefs

Cf. A297330, A297283, A297284.

Sequence in context: A040182 A335476 A296755 * A095782 A143204 A276525

Adjacent sequences: A297279 A297280 A297281 * A297283 A297284 A297285

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 17 2018

Status

approved