A297237 Down-variation of the base-13 digits of n; see Comments.

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

Offset

1,26

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

26 in base 13: 2,0; here DV = 2, so that a(26) = 2.

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. A297238, A297239, A297330.

Sequence in context: A297246 A297243 A297240 * A297234 A085857 A335824

Adjacent sequences: A297234 A297235 A297236 * A297238 A297239 A297240

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 17 2018

Status

approved