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A297246 Down-variation of the base-16 digits of n; see Comments. 4
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 4, 3, 2, 1, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,32

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

32 in base 15: 2,0; here DV = 2, so that a(32) = 2.

MATHEMATICA

g[n_, b_] := Differences[IntegerDigits[n, b]];

b = 16; z = 120; Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}];  (* A297246 *)

Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}]; (* A297247 *)

CROSSREFS

Cf. A297247, A297248, A297330.

Sequence in context: A130713 A236619 A300828 * A297243 A297240 A297237

Adjacent sequences:  A297243 A297244 A297245 * A297247 A297248 A297249

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling, Jan 18 2018

STATUS

approved

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Last modified June 15 16:13 EDT 2019. Contains 324142 sequences. (Running on oeis4.)