A297241 Up-variation of the base-14 digits of n; see Comments.

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

Offset

1,17

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

18 in base 14: 1,4; here UV = 3, so that a(18) = 3.

Mathematica

g[n_, b_] := Differences[IntegerDigits[n, b]];
b = 14; z = 120; Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}];  (* A297240 *)
Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}]; (* A297241 *)

Crossrefs

Cf. A297240, A297242, A297330.

Sequence in context: A254948 A072778 A178787 * A034326 A053833 A167973

Adjacent sequences: A297238 A297239 A297240 * A297242 A297243 A297244

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 17 2018

Status

approved