A297245 Total variation of base-15 digits of n; see Comments.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 5, 4, 3, 2, 1, 0, 1, 2, 3

Offset

1,18

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). 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

2^20 in base 15:  1, 5, 10, 10, 5, 1; here, DV = 9 and UV = 9, so that a(2^20) = 18.

Mathematica

b = 15; z = 120; t = Table[Total@Flatten@Map[Abs@Differences@# &,      Partition[IntegerDigits[n, b], 2, 1]], {n, z}] (* cf. Michael De Vlieger, e.g. A037834 *)

Crossrefs

Cf. A297243, A297244, A297330.

Sequence in context: A297244 A070696 A053834 * A043273 A268982 A278065

Adjacent sequences: A297242 A297243 A297244 * A297246 A297247 A297248

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 17 2018

Status

approved