A297289 Numbers whose base-16 digits have equal down-variation and up-variation; see Comments.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221, 238, 255, 257, 273, 289, 305, 321, 337, 353, 369, 385, 401, 417, 433, 449, 465, 481, 497, 514, 530, 546, 562, 578, 594, 610, 626, 642, 658, 674

Offset

1,2

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 A029730 after the zero first at 4113 = 1011_16 (not a base-16 palindrome), where DV=UV=1. - R. J. Mathar, Jan 23 2018

Links

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

Example

674 in base-16:  2,10,2 having DV = 8, UV = 8, so that 674 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 = 16; 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]   (* A297288 *)
Take[Flatten[Position[w, 0]], 120]    (* A297289 *)
Take[Flatten[Position[w, 1]], 120]    (* A297290 *)

Crossrefs

Cf. A297330, A297288, A297290.

Sequence in context: A043719 A296759 A029730 * A048327 A048340 A331026

Adjacent sequences: A297286 A297287 A297288 * A297290 A297291 A297292

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 17 2018

Status

approved