cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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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).

Original entry on oeis.org

1, 8, 48, 68, 1158, 4752, 81926, 1059600, 713949458, 299601649920
Offset: 1

Views

Author

Rémy Sigrist, Mar 26 2020

Keywords

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.
		

Crossrefs

Programs

  • PARI
    See Links section.

Formula

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

Extensions

a(10) from Giovanni Resta, Mar 30 2020
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