

A297236


Total variation of base12 digits of n; see Comments.


2



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

1,15


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

2^20 in base 12: 4, 2, 6, 9, 9, 4; here, DV = 7 and UV = 7, so that a(2^20) = 14.


MATHEMATICA

b = 12; 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. A297234, A297235, A297330.
Sequence in context: A137564 A056960 A227362 * A103693 A117230 A093882
Adjacent sequences: A297233 A297234 A297235 * A297237 A297238 A297239


KEYWORD

nonn,base,easy


AUTHOR

Clark Kimberling, Jan 17 2018


STATUS

approved



