A297240 Down-variation of the base-14 digits of n; see Comments.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 5, 4

Offset

1,28

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

28 in base 14: 2,0; here DV = 2, so that a(28) = 2.

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. A297241, A297242, A297330.

Sequence in context: A300828 A297246 A297243 * A297237 A297234 A085857

Adjacent sequences: A297237 A297238 A297239 * A297241 A297242 A297243

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 17 2018

Status

approved