A297238 Up-variation of the base-13 digits of n; see Comments.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 0, 0, 0, 0, 0, 0, 0, 1

Offset

1,16

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

17 in base 13: 1,4; here UV = 3, so that a(17) = 3.

Mathematica

g[n_, b_] := Differences[IntegerDigits[n, b]];
b = 13; z = 120; Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}];  (* A297237 *)
Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}]; (* A297238 *)

Crossrefs

Cf. A297237, A297239, A297330.

Sequence in context: A228722 A130024 A131232 * A010881 A190600 A053832

Adjacent sequences: A297235 A297236 A297237 * A297239 A297240 A297241

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 17 2018

Status

approved