A333522 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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