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A296882
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Numbers n whose base-10 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments.
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68
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67
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OFFSET
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1,2
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COMMENTS
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A pit is an index i such that d(i-1) > d(i) < d(i+1); a peak is an index i such that d(i-1) < d(i) > d(i+1). The sequences A296882-A296883 partition the natural numbers. See the guides at A296712. We have a(n) = A000027(n) for n=1..100 but not n=101.
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Guide to related sequences:
Base #(rises) = #(falls) #(rises) > #(falls) #(rises) < #(falls)
2 A296858 A296859 A296860
3 A296861 A296862 A296863
4 A296864 A296865 A296866
5 A296867 A296868 A296869
6 A296870 A296871 A296872
7 A296873 A296874 A296875
8 A296876 A296877 A296878
9 A296879 A296880 A296883
10 A296882 A296883 A296885
11 A296885 A296886 A296888
12 A296888 A296889 A296890
13 A296891 A296892 A296893
14 A296894 A296895 A296896
15 A296897 A296898 A296899
16 A296900 A296901 A296902
20 A296903 A296904 A296905
60 A296906 A296907 A296908
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LINKS
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Clark Kimberling, Table of n, a(n) for n = 1..10000
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EXAMPLE
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The base-10 digits of 1212 are 1,2,1,2; here #(pits) = 1 and #(peaks) = 1, so that 1212 is in the sequence.
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MATHEMATICA
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z = 200; b = 10;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &] (* A296882 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &] (* A296883 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &] (* A296884 *)
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CROSSREFS
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Cf. A296882, A296712, A296883, A296884.
Sequence in context: A258071 A266279 A296879 * A296885 A296888 A296891
Adjacent sequences: A296879 A296880 A296881 * A296883 A296884 A296885
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KEYWORD
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nonn,base,easy
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AUTHOR
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Clark Kimberling, Jan 10 2018
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STATUS
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approved
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