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Numbers whose base-20 digits d(m), d(m-1), ..., d(0) have #(pits) < #(peaks); see Comments.
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%I #16 Jan 21 2023 02:23:13

%S 440,441,460,461,462,480,481,482,483,500,501,502,503,504,520,521,522,

%T 523,524,525,540,541,542,543,544,545,546,560,561,562,563,564,565,566,

%U 567,580,581,582,583,584,585,586,587,588,600,601,602,603,604,605,606,607

%N Numbers whose base-20 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 A296903..A296905 partition the natural numbers. See the guides at A296712 and A296882.

%H Clark Kimberling, <a href="/A296905/b296905.txt">Table of n, a(n) for n = 1..10000</a>

%e The base-20 digits of 176441 are 1,2,1,2,1; here #(pits) = 1 and #(peaks) = 2, so 176441 is in the sequence.

%t z = 200; b = 20;

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

%t Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &] (* A296903 *)

%t Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &] (* A296904 *)

%t Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &] (* A296905 *)

%Y Cf. A296882, A296712, A296903, A296904.

%K nonn,base,easy

%O 1,1

%A _Clark Kimberling_, Jan 12 2018

%E b-file replaced by _Clark Kimberling_, Feb 27 2018