OFFSET
3,1
COMMENTS
Conjecture 1: The sequence contains only 1's and the primes.
Conjecture 2: Except for 2 and 3, all primes appear in the sequence once.
Conjecture: Record values correspond to A045375(m), m > 2. - Bill McEachen, Aug 03 2024
LINKS
Mohammed Bouras, The Distribution Of Prime Numbers And Continued Fractions, (ppt) (2022).
EXAMPLE
For n=3, 1/(2 - 3/(3 + 5)) = 8/13, so a(3)=13.
For n=4, 1/(2 - 3/(3 - 4/(4 + 5))) = 23/19, so a(4)=19.
For n=5, 1/(2 - 3/(3 - 4/(4 - 5/(5 + 5)))) = 13/5, so a(5)=5.
For n=6, 1/(2 - 3/(3 - 4/(4 - 5/(5 - 6/(6 + 5))))) = 227/31, so a(6)=31.
CROSSREFS
KEYWORD
nonn
AUTHOR
Mohammed Bouras, May 12 2024
STATUS
approved