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, 8, 48, 68, 1158, 4752, 81926, 1059600, 713949458, 299601649920

Offset: 1

Author

Rémy Sigrist, Mar 26 2020

Keywords

• nonn
• base
• more

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.

Examples

			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.
		

Links

• Rémy Sigrist, PARI program for A333522

Crossrefs

Cf. A052349, A333403.

Programs

PARI

See Links section.

Formula

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

Extensions

a(10) from Giovanni Resta, Mar 30 2020