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A296871 Numbers whose base-6 digits d(m), d(m-1), ..., d(0) have #(pits) > #(peaks); see Comments. 4

%I #12 Jan 23 2023 02:48:11

%S 37,38,39,40,41,73,74,75,76,77,80,81,82,83,109,110,111,112,113,116,

%T 117,118,119,123,124,125,145,146,147,148,149,152,153,154,155,159,160,

%U 161,166,167,181,182,183,184,185,188,189,190,191,195,196,197,202,203

%N Numbers whose base-6 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 A296870-A296872 partition the natural numbers. See the guides at A296882 and A296712.

%H Clark Kimberling, <a href="/A296871/b296871.txt">Table of n, a(n) for n = 1..10000</a>

%e The base-6 digits of 203 are 5,3,5; here #(pits) = 1 and #(peaks) = 0, so 203 is in the sequence.

%t z = 200; b = 6;

%t d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];

%t Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &] (* A296870 *)

%t Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &] (* A296871 *)

%t Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &] (* A296872 *)

%Y Cf. A296882, A296712, A296870, A296872.

%K nonn,base,easy

%O 1,1

%A _Clark Kimberling_, Jan 09 2018

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Last modified April 20 00:03 EDT 2024. Contains 371798 sequences. (Running on oeis4.)