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A297033 Number of pieces in the list d(m), d(m-1), ..., d(0) of base-5 digits of n; see Comments. 2
0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,25
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
EXAMPLE
Base-5 digits for 1234: 1, 4, 4, 1, 4, so that a(1234) = 4.
MATHEMATICA
a[n_, b_] := Length[Map[Length, Split[Sign[Differences[IntegerDigits[n, b]]]]]];
b = 5; Table[a[n, b], {n, 1, 120}]
CROSSREFS
Cf. A297030 (pieces), A296712 (rises and falls), A296882 (pits and peaks).
Sequence in context: A361338 A241927 A358619 * A342227 A194318 A306459
KEYWORD
nonn,easy,base
AUTHOR
Clark Kimberling, Jan 13 2018
STATUS
approved

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Last modified March 1 18:30 EST 2024. Contains 370443 sequences. (Running on oeis4.)