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 A296882 Numbers whose base-10 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments. 68
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. . Guide to related sequences: Base #(pits) = #(peaks) #(pits) > #(peaks) #(pits) < #(peaks) 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 A296881 10 A296882 A296883 A296884 11 A296885 A296886 A296887 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 LINKS Clark Kimberling, Table of n, a(n) for n = 1..10000 EXAMPLE The base-10 digits of 1212 are 1,2,1,2; here #(pits) = 1 and #(peaks) = 1, so 1212 is in the sequence. MATHEMATICA 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 *) CROSSREFS Cf. A296882, A296712, A296883, A296884. Sequence in context: A258071 A266279 A296879 * A296885 A296888 A296891 Adjacent sequences: A296879 A296880 A296881 * A296883 A296884 A296885 KEYWORD nonn,base,easy AUTHOR Clark Kimberling, Jan 10 2018 EXTENSIONS Overview table corrected by Georg Fischer, Aug 24 2021 STATUS approved

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Last modified February 5 16:28 EST 2023. Contains 360086 sequences. (Running on oeis4.)