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A296882 Numbers whose base-10 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments.

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