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A363102
Denominator of the continued fraction 1/(2-3/(3-4/(4-5/(...(n-1)-n/(-2))))).
2
7, 7, 23, 17, 47, 31, 79, 7, 17, 71, 167, 97, 223, 127, 41, 23, 359, 199, 439, 241, 31, 41, 89, 337, 727, 1, 839, 449, 137, 73, 1087, 577, 1223, 647, 1367, 103, 1, 47, 73, 881, 1847, 967, 1, 151, 2207, 1151, 2399, 1249, 113, 193, 401, 1, 3023, 1567, 191, 41, 71, 257, 3719, 113, 3967, 89, 103, 311
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OFFSET
3,1
COMMENTS
Conjecture 1: The sequence contains only 1's and primes.
Conjecture 2: All prime numbers appear either twice (same as A356247 and A357127) or three times.
Similar terms of A164314.
Conjecture: Record values correspond to A028871(m), m > 1. - Bill McEachen, Mar 06 2024
a(n) = 1 positions appear to correspond to A060515(m), m > 2. - Bill McEachen, Aug 05 2024
LINKS
Bill McEachen, Table of n, a(n) for n = 3..10002
Mohammed Bouras, The Distribution Of Prime Numbers And Continued Fractions, (ppt) (2022)
FORMULA
a(n) = (n^2 - 2)/gcd(n^2 - 2, 2*A051403(n-3) + n*A051403(n-4)).
a(n) = A164314(n) if A164314(n) > n.
If a(n) = a(m) and n < m < a(n), then a(n) = n + m.
EXAMPLE
a(5) = (5^2 - 2)/gcd(5^2 - 2, 2*A051403(5-3) + 5*A051403(5-4))= 23.
a(6) = a(11) = 6 + 11 = 17.
a(7) = a(40) = 7 + 40 = 47.
PROG
(PARI) a051403(n) = (n+2)*sum(k=0, n, k!)/2;
a(n) = (n^2 - 2)/gcd(n^2 - 2, 2*a051403(n-3) + n*a051403(n-4)); \\ Michel Marcus, May 24 2023
CROSSREFS
Cf. A008865, A051403, A059772, A164314, A356247, A357127.
Sequence in context: A283067 A284185 A059772 * A114369 A286858 A289370
Adjacent sequences: A363099 A363100 A363101 * A363103 A363104 A363105
KEYWORD
nonn
AUTHOR
Mohammed Bouras, May 19 2023
STATUS
approved

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Last modified October 4 23:29 EDT 2024. Contains 376525 sequences.
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