A370726 Denominator of the continued fraction 1/(2-3/(3-4/(4-5/(...(n-1)-n/(n+3))))).

3, 13, 17, 7, 5, 29, 11, 37, 41, 1, 7, 53, 19, 61, 1, 23, 73, 1, 1, 1, 89, 31, 97, 101, 1, 109, 113, 1, 1, 1, 43, 1, 137, 47, 1, 149, 1, 157, 1, 1, 1, 173, 59, 181, 1, 1, 193, 197, 67, 1, 1, 71, 1, 1, 1, 229, 233, 79, 241, 1, 83, 1, 257, 1, 1, 269, 1, 277

Offset

3,1

Comments

Conjecture: The sequence contains only 1's and the primes.

Conjecture: Record values correspond to A002144 (n>3). - Bill McEachen, May 21 2024

Links

Bill McEachen, Table of n, a(n) for n = 3..10002

Mohammed Bouras, The Distribution Of Prime Numbers And The Continued Fractions, (paper still under development) (2022).

Mohammed Bouras, The Distribution Of Prime Numbers And Continued Fractions, (ppt) (2022).

Formula

a(n) = (4n - 3)/gcd(4n - 3, A051403(n-2) + 3*A051403(n-3)).

Example

For n=3, 1/(2 - 3/(3 + 3)) = 2/3, so a(3)=3.
For n=4, 1/(2 - 3/(3 - 4/(4 + 3))) = 17/13, so a(4)=13.
For n=5, 1/(2 - 3/(3 - 4/(4 - 5/(5 + 3)))) = 49/17, so a(5)=17.

Crossrefs

Cf. A051403, A356360, A369797.

Sequence in context: A041815 A042589 A218364 * A107922 A119889 A038956

Adjacent sequences: A370723 A370724 A370725 * A370727 A370728 A370729

Keyword

nonn

Author

Mohammed Bouras, Feb 28 2024

Status

approved