A333522 - OEIS

%I #10 Mar 30 2020 03:46:59

%S 1,8,48,68,1158,4752,81926,1059600,713949458,299601649920

%N 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 This sequence is infinite (the proof is similar to that of the infinity of A333403).

%C This sequence has similarities with A052349; here we combine terms with the XOR operator, there with the classical addition.

%C All terms, except a(1) = 1, are even.

%H Rémy Sigrist, <a href="/A333522/a333522.gp.txt">PARI program for A333522</a>

%F a(n) = A333403(2^(n-1)).

%e For n = 1:

%e - we can choose a(1) = 1.

%e For n = 2:

%e - 2 is prime,

%e - 3 is prime,

%e - 4 XOR 1 = 5 is prime,

%e - 5 is prime,

%e - 6 XOR 1 = 7 is prime,

%e - 7 is prime,

%e - neither 8 nor 8 XOR 1 = 9 is prime,

%e - so a(2) = 8.

%o (PARI) See Links section.

%Y Cf. A052349, A333403.

%K nonn,base,more

%O 1,2

%A _Rémy Sigrist_, Mar 26 2020

%E a(10) from _Giovanni Resta_, Mar 30 2020