A297244 Up-variation of the base-15 digits of n; see Comments.

0, 0, 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, 12, 13, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 0, 0, 0, 0, 0, 1, 2, 3

Offset

1,18

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

19 in base 15: 1,4; here UV = 3, so that a(19) = 3.

Mathematica

g[n_, b_] := Differences[IntegerDigits[n, b]];
b = 15; z = 120; Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}];  (* A297243 *)
Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}]; (* A297244 *)

Crossrefs

Cf. A297243, A297245, A297330.

Sequence in context: A357030 A303219 A071523 * A070696 A053834 A297245

Adjacent sequences: A297241 A297242 A297243 * A297245 A297246 A297247

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 17 2018

Status

approved