A297231 Down-variation of the base-11 digits of n; see Comments.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 5, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 6, 5, 4, 3, 2, 1, 0, 0, 0, 0, 0, 7, 6, 5, 4, 3, 2, 1, 0, 0, 0

Offset

1,22

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

22 in base 11: 2,0; here DV = 2, so that a(22) = 2.

Mathematica

g[n_, b_] := Differences[IntegerDigits[n, b]];
b = 11; z = 120; Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}];  (* A297231 *)
Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}]; (* A297232 *)

Crossrefs

Cf. A297232, A297233, A297330.

Sequence in context: A297234 A085857 A335824 * A056620 A316869 A351961

Adjacent sequences: A297228 A297229 A297230 * A297232 A297233 A297234

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 17 2018

Status

approved