login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A297248 Total variation of base-16 digits of n; see Comments. 3
0, 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, 14, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 5, 4, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,19

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

3^10 in base 16:  14, 6, 10, 9; here, DV = 9 and UV = 4, so that a(2^20) = 13.

MATHEMATICA

b = 16; 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. A297246, A297247, A297330.

Sequence in context: A167463 A053835 A072965 * A043274 A318891 A318890

Adjacent sequences:  A297245 A297246 A297247 * A297249 A297250 A297251

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling, Jan 17 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 19 00:55 EDT 2019. Contains 324217 sequences. (Running on oeis4.)