A297232 Up-variation of the base-11 digits of n; see Comments.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2

Offset

1,14

Comments

Suppose that a number 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). Every positive integer occurs infinitely many times. See A297330 for a guide to related sequences and partitions of the natural numbers.

Links

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

Example

15 in base 11: 1,4; here UV = 3, so that a(15) = 3.

Mathematica

g[n_, b_] := Differences[IntegerDigits[n, b]];
b = 11; z = 120; Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}];  (* A297231 *)
Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}]; (* A297232 *)

Crossrefs

Cf. A297231, A297233, A297330.

Sequence in context: A128557 A265542 A103303 * A093691 A004176 A085124

Adjacent sequences: A297229 A297230 A297231 * A297233 A297234 A297235

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 17 2018

Status

approved