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A297247
Up-variation of the base-16 digits of n; see Comments.
4
0, 0, 0, 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, 12, 13, 14, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0, 0, 0
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
EXAMPLE
20 in base 16: 1,4; here UV = 3, so that a(20) = 3.
MATHEMATICA
g[n_, b_] := Differences[IntegerDigits[n, b]];
b = 16; z = 120; Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}]; (* A297246 *)
Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}]; (* A297247 *)
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Clark Kimberling, Jan 18 2018
STATUS
approved