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 A296889 Numbers whose base-12 digits d(m), d(m-1), ..., d(0) have #(pits) > #(peaks); see Comments. 4

%I #7 Jan 21 2023 19:48:51

%S 145,146,147,148,149,150,151,152,153,154,155,289,290,291,292,293,294,

%T 295,296,297,298,299,302,303,304,305,306,307,308,309,310,311,433,434,

%U 435,436,437,438,439,440,441,442,443,446,447,448,449,450,451,452,453,454

%N Numbers whose base-12 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 A296888-A296890 partition the natural numbers. See the guides at A296712 and A296882.

%H Clark Kimberling, <a href="/A296889/b296889.txt">Table of n, a(n) for n = 1..10000</a>

%e The base-12 digits of 43502 are 2,1,2,1,2; here #(pits) = 2 and #(peaks) = 1, so 43502 is in the sequence.

%t z = 200; b = 12;

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

%t Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &] (* A296888 *)

%t Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &] (* A296889 *)

%t Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &] (* A296890 *)

%Y Cf. A296882, A296712, A296888, A296890.

%K nonn,base,easy

%O 1,1

%A _Clark Kimberling_, Jan 10 2018

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Last modified July 13 12:36 EDT 2024. Contains 374284 sequences. (Running on oeis4.)