

A297246


Downvariation of the base16 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
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OFFSET

1,32


COMMENTS

Suppose that a number n has baseb digits b(m), b(m1), ..., b(0). The baseb downvariation of n is the sum DV(n,b) of all d(i)d(i1) for which d(i) > d(i1); the baseb upvariation of n is the sum UV(n,b) of all d(k1)d(k) for which d(k) < d(k1). The total baseb 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



