A357057 a(n) = A356886(2^n+1)/A356886(2^n-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

Author

Paul Curtz, Sep 09 2022

Keywords

• nonn
• more

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. A000051, A000225, A356886.

Cf. also A065091 (odd primes).

Extensions

a(14)-a(24) from Michel Marcus, Sep 13 2022

a(25)-a(31) from Chai Wah Wu, Oct 01 2022