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A297041 Number of pieces in the list d(m),d(m-1),...,d(0) of base-13 digits of n; see Comments 2
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

The definition of "piece" starts with the base-b digits d(m), d(m-1), ..., d(0) of n.  First, an *ascent* is a list (d(i),d(i-1),...,d(i-h)) such that d(i)<d(i-1)<...<d(i-h), where d(i+1)>=d(i) if i<m, and d(i-h-1)>=d(i-h) if i>h.  A *descent* is a list (d(i),d(i-1),...,d(i-h)) such that d(i)>d(i-1)>...>d(i-h), where d(i+1)<=d(i) if i<m, and d(i-h-1)<=d(i-h) if i>h.  A *flat* is a list (d(i),d(i-1),...,d(i-h)), where h>0, such that d(i)=d(i-1)=...=d(i-h), where d(i+1)!=d(i) if i<m, and d(i-h-1)!=d(i-h) if i>h. A *piece* is an ascent, a descent, or a flat.  Example:  235621103 has five pieces:  (2,3,5,6), (6,2,1), (1,1), (1,0), and (0,3); that's 2 ascents, 2 descents, and 1 flat. For every b, the "piece sequence" includes every positive integer infinitely many times. See A297030 for a guide to related sequences.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000

EXAMPLE

Base-13 digits for 1234567:  3, 4, 2, 12, 1, 9, so that a(124567) = 5.

MATHEMATICA

a[n_, b_] := Length[Map[Length, Split[Sign[Differences[IntegerDigits[n, b]]]]]];

b = 13; Table[a[n, b], {n, 1, 1000}]

CROSSREFS

Cf. A297030 (pieces), A296712 (rises and falls), A296882 (pits and peaks).

Sequence in context: A277160 A277163 A011726 * A070109 A107846 A179801

Adjacent sequences:  A297038 A297039 A297040 * A297042 A297043 A297044

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Jan 13 2018

STATUS

approved

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Last modified April 14 18:48 EDT 2021. Contains 342951 sequences. (Running on oeis4.)