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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). 1
 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 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

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Last modified August 15 12:59 EDT 2020. Contains 336502 sequences. (Running on oeis4.)