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%I #13 Jan 21 2023 20:28:25
%S 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,
%T 27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,
%U 50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67
%N Numbers whose base-10 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments.
%C 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.
%C .
%C Guide to related sequences:
%C Base #(pits) = #(peaks) #(pits) > #(peaks) #(pits) < #(peaks)
%C 2 A296858 A296859 A296860
%C 3 A296861 A296862 A296863
%C 4 A296864 A296865 A296866
%C 5 A296867 A296868 A296869
%C 6 A296870 A296871 A296872
%C 7 A296873 A296874 A296875
%C 8 A296876 A296877 A296878
%C 9 A296879 A296880 A296881
%C 10 A296882 A296883 A296884
%C 11 A296885 A296886 A296887
%C 12 A296888 A296889 A296890
%C 13 A296891 A296892 A296893
%C 14 A296894 A296895 A296896
%C 15 A296897 A296898 A296899
%C 16 A296900 A296901 A296902
%C 20 A296903 A296904 A296905
%C 60 A296906 A296907 A296908
%H Clark Kimberling, <a href="/A296882/b296882.txt">Table of n, a(n) for n = 1..10000</a>
%e The base-10 digits of 1212 are 1,2,1,2; here #(pits) = 1 and #(peaks) = 1, so 1212 is in the sequence.
%t z = 200; b = 10;
%t d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
%t Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &] (* A296882 *)
%t Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &] (* A296883 *)
%t Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &] (* A296884 *)
%Y Cf. A296882, A296712, A296883, A296884.
%K nonn,base,easy
%O 1,2
%A _Clark Kimberling_, Jan 10 2018
%E Overview table corrected by _Georg Fischer_, Aug 24 2021
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