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