cp's OEIS Frontend

A333522 Lexicographically earliest sequence of distinct positive integers such that for any nonempty set of k positive integers, say {m_1, ..., m_k}, a(m_1) XOR ... XOR a(m_k) is neither null nor prime (where XOR denotes the bitwise XOR operator).

%I A333522 #10 Mar 30 2020 03:46:59
%S A333522 1,8,48,68,1158,4752,81926,1059600,713949458,299601649920
%N A333522 Lexicographically earliest sequence of distinct positive integers such that for any nonempty set of k positive integers, say {m_1, ..., m_k}, a(m_1) XOR ... XOR a(m_k) is neither null nor prime (where XOR denotes the bitwise XOR operator).
%C A333522 This sequence is infinite (the proof is similar to that of the infinity of A333403).
%C A333522 This sequence has similarities with A052349; here we combine terms with the XOR operator, there with the classical addition.
%C A333522 All terms, except a(1) = 1, are even.
%H A333522 Rémy Sigrist, <a href="/A333522/a333522.gp.txt">PARI program for A333522</a>
%F A333522 a(n) = A333403(2^(n-1)).
%e A333522 For n = 1:
%e A333522 - we can choose a(1) = 1.
%e A333522 For n = 2:
%e A333522 - 2 is prime,
%e A333522 - 3 is prime,
%e A333522 - 4 XOR 1 = 5 is prime,
%e A333522 - 5 is prime,
%e A333522 - 6 XOR 1 = 7 is prime,
%e A333522 - 7 is prime,
%e A333522 - neither 8 nor 8 XOR 1 = 9 is prime,
%e A333522 - so a(2) = 8.
%o A333522 (PARI) See Links section.
%Y A333522 Cf. A052349, A333403.
%K A333522 nonn,base,more
%O A333522 1,2
%A A333522 _Rémy Sigrist_, Mar 26 2020
%E A333522 a(10) from _Giovanni Resta_, Mar 30 2020