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A296908 Numbers whose base-60 digits d(m), d(m-1), ..., d(0) have #(pits) < #(peaks); see Comments. 4

%I #16 Jan 21 2023 03:00:00

%S 3720,3721,3780,3781,3782,3840,3841,3842,3843,3900,3901,3902,3903,

%T 3904,3960,3961,3962,3963,3964,3965,4020,4021,4022,4023,4024,4025,

%U 4026,4080,4081,4082,4083,4084,4085,4086,4087,4140,4141,4142,4143,4144,4145,4146,4147

%N Numbers whose base-60 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 A296906..A296908 partition the natural numbers. See the guides at A296712 and A296882.

%H Clark Kimberling, <a href="/A296908/b296908.txt">Table of n, a(n) for n = 1..10000</a>

%e The base-60 digits of 13395721 are 1,2,1,2,1; here #(pits) = 1 and #(peaks) = 2, so 13395721 is in the sequence.

%t z = 200; b = 60;

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

%t Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &] (* A296906 *)

%t Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &] (* A296907 *)

%t Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &] (* A296908 *)

%Y Cf. A296882, A296712, A296906, A296907.

%K nonn,base,easy

%O 1,1

%A _Clark Kimberling_, Jan 12 2018

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Last modified March 28 14:13 EDT 2024. Contains 371254 sequences. (Running on oeis4.)