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A324608 Number of 1's in binary expansion of A308092(n).

%I A324608 #20 Apr 10 2021 16:36:34
%S A324608 1,1,2,3,3,3,3,3,3,3,3,10,11,11,11,13,13,14,14,14,16,16,16,17,17,17,
%T A324608 19,19,19,19,20,20,20,22,22,22,22,22,23,23,23,25,25,25,25,25,25,26,26,
%U A324608 26,28,28,28,28,28,28,28,29,29,30,31,31,31,31,31,31,31,31
%N A324608 Number of 1's in binary expansion of A308092(n).
%C A324608 Conjecture: sequence is weakly increasing.
%H A324608 Robert Israel, <a href="/A324608/b324608.txt">Table of n, a(n) for n = 1..3000</a>
%F A324608 a(n) = A000120(A308092(n)).
%p A324608 S:= "110":
%p A324608 b("0"):= 0: b("1"):= 1:
%p A324608 A308092[1]:= 1: A308092[2]:= 2: t:= 3:
%p A324608 for n from 3 to 300 do
%p A324608   tp:= add(b(S[i])*2^(n-i),i=1..n);
%p A324608   A308092[n]:= tp - t;
%p A324608   t:= tp;
%p A324608   S:= cat(S,convert(A308092[n],binary));
%p A324608 od:
%p A324608 seq(convert(convert(A308092[n],base,2),`+`), n=1..300); # _Robert Israel_, Jun 12 2019
%t A324608 a[1]=1;a[2]=2;a[n_]:=a[n]=FromDigits[Flatten[IntegerDigits[#,2]&/@Table[a[k],{k,n-1}]][[;;n]],2]-Total@Table[a[m],{m,n-1}]
%t A324608 Count[#,1]&/@Table[IntegerDigits[a[l],2],{l,70}] (* _Giorgos Kalogeropoulos_, Mar 30 2021 *)
%o A324608 (Python)
%o A324608 def aupton(terms):
%o A324608   alst, bstr = [1, 1], "110"
%o A324608   for n in range(3, terms+1):
%o A324608     an = int(bstr[:n], 2) - int(bstr[:n-1], 2)
%o A324608     binan = bin(an)[2:]
%o A324608     alst, bstr = alst + [binan.count('1')], bstr + binan
%o A324608   return alst
%o A324608 print(aupton(68)) # _Michael S. Branicky_, Mar 30 2021
%Y A324608 Cf. A000120, A308092.
%K A324608 nonn,base
%O A324608 1,3
%A A324608 _Peter Kagey_, Jun 10 2019