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A297231
Down-variation of the base-11 digits of n; see Comments.
4
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 0, 5, 4, 3, 2, 1, 0, 0, 0, 0, 0, 0, 6, 5, 4, 3, 2, 1, 0, 0, 0, 0, 0, 7, 6, 5, 4, 3, 2, 1, 0, 0, 0
OFFSET
1,22
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
22 in base 11: 2,0; here DV = 2, so that a(22) = 2.
MATHEMATICA
g[n_, b_] := Differences[IntegerDigits[n, b]];
b = 11; z = 120; Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}]; (* A297231 *)
Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}]; (* A297232 *)
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Clark Kimberling, Jan 17 2018
STATUS
approved