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A297239 Total variation of base-13 digits of n; see Comments. 4
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, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,16

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 13:  2, 10, 9, 3, 7, 9; here, DV = 12 and UV = 9, so that a(2^20) = 21.

MATHEMATICA

b = 13; 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. A297237, A297238, A297330.

Sequence in context: A053832 A322094 A056961 * A043271 A333921 A278063

Adjacent sequences:  A297236 A297237 A297238 * A297240 A297241 A297242

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling, Jan 17 2018

STATUS

approved

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Last modified June 17 16:32 EDT 2021. Contains 345085 sequences. (Running on oeis4.)