OFFSET
1,19
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). 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
20 in base 16: 1,4; here UV = 3, so that a(20) = 3.
MATHEMATICA
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Clark Kimberling, Jan 18 2018
STATUS
approved