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 A297030 Number of pieces in the list d(m),d(m-1),...,d(0) of base-2 digits of n; see Comments 17
 0, 1, 1, 2, 2, 2, 1, 2, 3, 3, 3, 3, 3, 2, 1, 2, 3, 4, 4, 4, 4, 4, 3, 3, 4, 4, 4, 3, 3, 2, 1, 2, 3, 4, 4, 5, 5, 5, 4, 4, 5, 5, 5, 5, 5, 4, 3, 3, 4, 5, 5, 5, 5, 5, 4, 3, 4, 4, 4, 3, 3, 2, 1, 2, 3, 4, 4, 5, 5, 5, 4, 5, 6, 6, 6, 6, 6, 5, 4, 4, 5, 6, 6, 6, 6, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 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) if i=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 ih.  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 ih. 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. Guide to related sequences: *** Base   # pieces for n>=1 2         A297030 3         A297031 4         A297032 5         A297033 6         A297034 7         A297035 8         A297036 9         A297037 10        A297038 11        A297039 12        A297040 13        A297041 14        A297042 15        A297043 16        A297044 20        A297045 60        A297046 LINKS Clark Kimberling, Table of n, a(n) for n = 1..10000 EXAMPLE Base-2 digits for 100:  1, 1, 0, 0, 1, 0, 0, so that a(100) = 6. MATHEMATICA a[n_, b_] := Length[Map[Length, Split[Sign[Differences[IntegerDigits[n, b]]]]]]; b = 2; Table[a[n, b], {n, 1, 120}] CROSSREFS Cf. A297038, A296712 (rises and falls), A296882 (pits and peaks). Sequence in context: A205011 A130790 A261904 * A266348 A179647 A029330 Adjacent sequences:  A297027 A297028 A297029 * A297031 A297032 A297033 KEYWORD nonn,easy,base AUTHOR Clark Kimberling, Jan 13 2018 STATUS approved

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Last modified January 17 23:00 EST 2021. Contains 340247 sequences. (Running on oeis4.)