A297246 Down-variation of the base-16 digits of n; see Comments.

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

Offset

1,32

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

32 in base 15: 2,0; here DV = 2, so that a(32) = 2.

Mathematica

g[n_, b_] := Differences[IntegerDigits[n, b]];
b = 16; z = 120; Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}];  (* A297246 *)
Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}]; (* A297247 *)

Crossrefs

Cf. A297247, A297248, A297330.

Sequence in context: A236619 A355627 A300828 * A297243 A297240 A297237

Adjacent sequences: A297243 A297244 A297245 * A297247 A297248 A297249

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 18 2018

Status

approved