A296859 - OEIS

%I #17 May 11 2021 08:44:59

%S 5,11,13,21,22,23,27,29,43,44,45,46,47,53,54,55,59,61,77,85,86,87,88,

%T 89,90,91,92,93,94,95,107,108,109,110,111,117,118,119,123,125,141,155,

%U 157,171,172,173,174,175,176,177,179,180,181,182,183,184,185,186

%N Numbers whose base-2 digits 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 A296858-A296860 partition the natural numbers. See the guides at A296882 and A296712.

%H Clark Kimberling, <a href="/A296859/b296859.txt">Table of n, a(n) for n = 1..10000</a>

%e The base-2 digits of 186 are 1,0,1,1,1,0,1,0; here #(pits) = 2 and #(peaks) = 1, so 186 is in the sequence.

%t z = 200; b = 2;

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

%t Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296858 *)

%t Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296859 *)

%t Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296860 *)

%o (Python)

%o def cwo(subs, s): # count with overlaps allowed

%o   c = i = 0

%o   while i != -1:

%o     i = s.find(subs, i)

%o     if i != -1: c += 1; i += 1

%o   return c

%o def ok(n): b = bin(n)[2:]; return cwo('101', b) > cwo('010', b)

%o print(list(filter(ok, range(1, 187)))) # _Michael S. Branicky_, May 11 2021

%Y Cf. A296882, A296712, A296858, A296860.

%K nonn,base,easy

%O 1,1

%A _Clark Kimberling_, Jan 09 2018