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A296874 Numbers whose base-7 digits d(m), d(m-1), ..., d(0) have #(pits) > #(peaks); see Comments. 4

%I #7 Jan 21 2023 18:11:01

%S 50,51,52,53,54,55,99,100,101,102,103,104,107,108,109,110,111,148,149,

%T 150,151,152,153,156,157,158,159,160,164,165,166,167,197,198,199,200,

%U 201,202,205,206,207,208,209,213,214,215,216,221,222,223,246,247,248

%N Numbers whose base-7 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 A296873-A296875 partition the natural numbers. See the guides at A296882 and A296712.

%H Clark Kimberling, <a href="/A296874/b296874.txt">Table of n, a(n) for n = 1..9999</a>

%e The base-7 digits of 248 are 5,0,3; here #(pits) = 0 and #(peaks) = 0, so 248 is in the sequence.

%t z = 200; b = 7;

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

%t Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &] (* A296873 *)

%t Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &] (* A296874 *)

%t Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &] (* A296875 *)

%Y Cf. A296882, A296712, A296873, A296875.

%K nonn,base,easy

%O 1,1

%A _Clark Kimberling_, Jan 09 2018

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Last modified May 21 05:34 EDT 2024. Contains 372728 sequences. (Running on oeis4.)