OFFSET
1,15
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). 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
KEYWORD
nonn,base,easy
AUTHOR
Clark Kimberling, Jan 17 2018
STATUS
approved