A297234 Down-variation of the base-12 digits of n; see Comments.

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

Offset

1,24

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

24 in base 12: 2,0; here DV = 2, so that a(24) = 2.

Mathematica

g[n_, b_] := Differences[IntegerDigits[n, b]];
b = 12; z = 120; Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}];  (* A297234 *)
Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}]; (* A297235 *)

Crossrefs

Cf. A297234, A297235, A297330.

Sequence in context: A297243 A297240 A297237 * A085857 A335824 A297231

Adjacent sequences: A297231 A297232 A297233 * A297235 A297236 A297237

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 17 2018

Status

approved