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

1,2

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^(n-1)).

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