cp's OEIS Frontend

A285103 Number of odd terms on row n of A053632: a(n) = A000120(A068052(n)).

%I A285103 #32 May 18 2024 01:54:42
%S A285103 1,2,4,6,6,12,12,16,22,28,32,30,36,52,48,62,62,68,88,104,116,108,128,
%T A285103 128,132,168,160,168,200,204,240,232,242,284,300,324,332,348,352,352,
%U A285103 412,440,400,466,460,516,496,566,582,580,608,646,676,736,716,782,728,816,832,856,916,924,948,1034,1008,1044,1096,1154,1112,1212,1204,1188
%N A285103 Number of odd terms on row n of A053632: a(n) = A000120(A068052(n)).
%H A285103 Alois P. Heinz, <a href="/A285103/b285103.txt">Table of n, a(n) for n = 0..5000</a> (first 257 terms from Antti Karttunen)
%F A285103 a(n) = A000120(A068052(n)).
%F A285103 a(n) = A001221(A285102(n)) = A001222(A285102(n)).
%F A285103 A285104(n) = 2^n - a(n).
%F A285103 A000124(n) = a(n) + A285105(n).
%p A285103 b:= proc(n) option remember; `if`(n=0, 1,
%p A285103       (t-> Bits[Xor](2^n*t, t))(b(n-1)))
%p A285103     end:
%p A285103 a:= n-> convert(Bits[Split](b(n)), `+`):
%p A285103 seq(a(n), n=0..71);  # _Alois P. Heinz_, Mar 07 2024
%t A285103 b[n_] := b[n] = If[n == 0, 1, With[{t = b[n-1]}, BitXor[2^n*t, t]]];
%t A285103 a[n_] := DigitCount[b[n], 2, 1];
%t A285103 Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, May 17 2024, after _Alois P. Heinz_ *)
%o A285103 (Scheme) (define (A285103 n) (A000120 (A068052 n)))
%o A285103 (Python) # uses [A000120]
%o A285103 l=[1]
%o A285103 for n in range(1, 101):
%o A285103     x = l[n - 1]
%o A285103     l.append(x^(2**n*x))
%o A285103 print([A000120(k) for k in l]) # _Indranil Ghosh_, Jun 28 2017
%Y A285103 Number of odd term on row n of A053632.
%Y A285103 Cf. A000120, A000124, A001221, A001222, A068052, A285102, A285104, A285105.
%K A285103 nonn
%O A285103 0,2
%A A285103 _Antti Karttunen_, Apr 15 2017