

A297238


Upvariation of the base13 digits of n; see Comments.


4



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

1,16


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

17 in base 13: 1,4; here UV = 3, so that a(17) = 3.


MATHEMATICA

g[n_, b_] := Differences[IntegerDigits[n, b]];
b = 13; z = 120; Table[Total[Select[g[n, b], # < 0 &]], {n, 1, z}]; (* A297237 *)
Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}]; (* A297238 *)


CROSSREFS

Cf. A297237, A297239, A297330.
Sequence in context: A228722 A130024 A131232 * A010881 A190600 A053832
Adjacent sequences: A297235 A297236 A297237 * A297239 A297240 A297241


KEYWORD

nonn,base,easy


AUTHOR

Clark Kimberling, Jan 17 2018


STATUS

approved



