A297283 Numbers whose base-14 digits have equal down-variation and up-variation; see Comments.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 197, 211, 225, 239, 253, 267, 281, 295, 309, 323, 337, 351, 365, 379, 394, 408, 422, 436, 450, 464, 478, 492, 506, 520, 534, 548, 562, 576, 591, 605, 619

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 first from A029959 after the zero for 2759 = 1011_14, which is not a palindrome in base 14 but has UV(2759,14) = DV(2759,14) = 1. - R. J. Mathar, Jan 23 2018

Links

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

Example

619 in base-14:  3,2,3 having DV = 1, UV = 1, so that 619 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, A297282, A297284.

Sequence in context: A043717 A296753 A029959 * A048325 A048338 A262524

Adjacent sequences: A297280 A297281 A297282 * A297284 A297285 A297286

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 17 2018

Status

approved