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A296869 Numbers whose base-5 digits d(m), d(m-1), ..., d(0) have #(pits) < #(peaks); see Comments.

%I A296869 #9 Jan 22 2023 20:51:11
%S A296869 35,36,40,41,42,45,46,47,48,65,66,67,70,71,72,73,95,96,97,98,160,161,
%T A296869 165,166,167,170,171,172,173,175,180,181,190,191,192,195,196,197,198,
%U A296869 200,205,206,210,211,212,220,221,222,223,225,230,231,235,236,237,240
%N A296869 Numbers whose base-5 digits d(m), d(m-1), ..., d(0) have #(pits) < #(peaks); see Comments.
%C A296869 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 A296867-A296869 partition the natural numbers. See the guides at A296882 and A296712.
%H A296869 Clark Kimberling, <a href="/A296869/b296869.txt">Table of n, a(n) for n = 1..10000</a>
%e A296869 The base-5 digits of 240 are 1,4,3,0; here #(pits) = 0 and #(peaks) = 1, so 240 is in the sequence.
%t A296869 z = 200; b = 5;
%t A296869 d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
%t A296869 Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296867 *)
%t A296869 Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296868 *)
%t A296869 Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296869 *)
%t A296869 updnQ[n_]:=Total[Which[#[[1]]<#[[2]]>#[[3]],1,#[[1]]>#[[2]]<#[[3]],-1,True,0]&/@Partition[IntegerDigits[n,5],3,1]]>0; Select[Range[ 250],updnQ] (* _Harvey P. Dale_, Dec 20 2020 *)
%Y A296869 Cf. A296882, A296712, A296867, A296868.
%K A296869 nonn,base,easy
%O A296869 1,1
%A A296869 _Clark Kimberling_, Jan 09 2018