

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).


1




OFFSET

1,2


COMMENTS

This sequence is infinite (the proof is similar to that of the infinity of A333403).
This sequence has similarities with A052349; here we combine terms with the XOR operator, there with the classical addition.
All terms, except a(1) = 1, are even.


LINKS

Table of n, a(n) for n=1..10.
Rémy Sigrist, PARI program for A333522


FORMULA

a(n) = A333403(2^(n1)).


EXAMPLE

For n = 1:
 we can choose a(1) = 1.
For n = 2:
 2 is prime,
 3 is prime,
 4 XOR 1 = 5 is prime,
 5 is prime,
 6 XOR 1 = 7 is prime,
 7 is prime,
 neither 8 nor 8 XOR 1 = 9 is prime,
 so a(2) = 8.


PROG

(PARI) See Links section.


CROSSREFS

Cf. A052349, A333403.
Sequence in context: A263506 A216323 A335351 * A165037 A121028 A139279
Adjacent sequences: A333519 A333520 A333521 * A333523 A333524 A333525


KEYWORD

nonn,base,more


AUTHOR

Rémy Sigrist, Mar 26 2020


EXTENSIONS

a(10) from Giovanni Resta, Mar 30 2020


STATUS

approved



