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A379375 a(n) is the number of coincidences between the sequence thus far and its terms rearranged in descending order.

%I A379375 #20 Jan 03 2025 11:47:29
%S A379375 0,1,0,1,2,1,2,1,2,2,2,3,2,3,2,3,4,5,4,5,4,5,4,3,2,2,2,2,2,2,2,3,5,5,
%T A379375 7,7,9,9,9,8,8,7,8,8,10,9,8,8,7,6,4,3,4,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,
%U A379375 3,3,3,3,4,4,4,4,4,4,4,5,7,7,7,8,8,9,9
%N A379375 a(n) is the number of coincidences between the sequence thus far and its terms rearranged in descending order.
%C A379375 Equivalently, this is the number of coincidences between the reverse of the sequence and its terms rearranged in ascending order.
%C A379375 A379250 is a variant beginning with 1.
%H A379375 Neal Gersh Tolunsky, <a href="/A379375/b379375.txt">Table of n, a(n) for n = 1..10000</a>
%H A379375 Neal Gersh Tolunsky, <a href="/A379375/a379375.png">Graph of 100000 terms</a>
%e A379375 To find a(5), we compare the first 4 terms of the sequence with the same terms arranged in descending order:
%e A379375 0, 1, 0, 1
%e A379375 1, 1, 0, 0
%e A379375    ^  ^
%e A379375 We find 2 coincidences, so a(5) = 2.
%p A379375 A:= [0]:
%p A379375 S:= [0]:
%p A379375 for n from 2 to 100 do
%p A379375   m:= numboccur(0,A+S);
%p A379375   A:= [op(A),m];
%p A379375   j:= ListTools:-BinaryPlace(S,-m);
%p A379375   S:= [op(S[1..j]),-m,op(S[j+1..-1])];
%p A379375 od:
%p A379375 A; # _Robert Israel_, Dec 22 2024
%t A379375 Nest[Append[#,Count[#-Reverse[Sort[#]],0]]&,{},87] (* _James C. McMahon_, Jan 03 2025 *)
%o A379375 (Python)
%o A379375 from bisect import insort
%o A379375 from itertools import islice
%o A379375 def agen(): # generator of terms
%o A379375     a, d, an = [], [], 0
%o A379375     while True:
%o A379375         a.append(an)
%o A379375         insort(d, an, key=lambda x: -x)
%o A379375         yield an
%o A379375         an = sum(1 for x, y in zip(a, d) if x == y)
%o A379375 print(list(islice(agen(), 87))) # _Michael S. Branicky_, Dec 21 2024
%Y A379375 Cf. A379250.
%K A379375 nonn
%O A379375 1,5
%A A379375 _Neal Gersh Tolunsky_, Dec 21 2024