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A297238 Up-variation of the base-13 digits of n; see Comments. 4
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, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 0, 0, 0, 0, 0, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,16

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

17 in base 13: 1,4; here UV = 3, so that a(17) = 3.

MATHEMATICA

g[n_, b_] := Differences[IntegerDigits[n, b]];

b = 13; z = 120; Table[-Total[Select[g[n, b], # < 0 &]], {n, 1, z}];  (* A297237 *)

Table[Total[Select[g[n, b], # > 0 &]], {n, 1, z}]; (* A297238 *)

CROSSREFS

Cf. A297237, A297239, A297330.

Sequence in context: A228722 A130024 A131232 * A010881 A190600 A053832

Adjacent sequences:  A297235 A297236 A297237 * A297239 A297240 A297241

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling, Jan 17 2018

STATUS

approved

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Last modified November 26 12:19 EST 2020. Contains 338639 sequences. (Running on oeis4.)