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A357057
a(n) = A356886(2^n+1)/A356886(2^n-1).
1
3, 3, 3, 5, 5, 7, 11, 11, 13, 17, 19, 19, 23, 29, 31, 37, 37, 41, 43, 47, 53, 59, 59, 61, 67, 71, 73, 79, 83, 83, 89
OFFSET
1,1
COMMENTS
All terms are odd primes; some of them are repeated.
Conjecture: This sequence has the pattern: a prime repeated, a run of m times primes standing alone, the next prime repeated, a run of m+1 times primes standing alone, ... . All primes will be repeated once or follow in sequence. We know that if A356886(2^n-1) = p1 then A356886(2^n+1) will be p1*p2. p2 will be the smallest possible prime such that p1*p2 is not yet in the sequence A356886, thus p2 = a(n). Let p1*pn be already in A356886 and pn < p2, then we know that p1*pn will be on a position A356886(2^n-(2^(k+1)-2)) with some k > 0. This should explain this pattern. - Thomas Scheuerle, Sep 14 2022
CROSSREFS
Cf. also A065091 (odd primes).
Sequence in context: A077886 A096015 A046702 * A226592 A133683 A182998
KEYWORD
nonn,more
AUTHOR
Paul Curtz, Sep 09 2022
EXTENSIONS
a(14)-a(24) from Michel Marcus, Sep 13 2022
a(25)-a(31) from Chai Wah Wu, Oct 01 2022
STATUS
approved