

A297248


Total variation of base16 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
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OFFSET

1,19


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). 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



