A370726 - OEIS

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

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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)).