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A369797
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Denominator of the continued fraction 1/(2-3/(3-4/(4-5/(...(n-1)-n/(n+2))))).
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2
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7, 5, 13, 2, 19, 11, 5, 1, 31, 17, 37, 1, 43, 23, 1, 1, 1, 29, 61, 1, 67, 1, 73, 1, 79, 41, 1, 1, 1, 47, 97, 1, 103, 53, 109, 1, 1, 59, 1, 1, 127, 1, 1, 1, 139, 71, 1, 1, 151, 1, 157, 1, 163, 83, 1, 1, 1, 89, 181, 1, 1, 1, 193, 1, 199, 101, 1, 1, 211
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OFFSET
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3,1
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COMMENTS
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Conjecture: The sequence contains only 1's and the primes.
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LINKS
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FORMULA
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EXAMPLE
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For n=3, 1/(2 - 3/(3 + 2)) = 5/7, so a(3)=7.
For n=4, 1/(2 - 3/(3 - 4/(4 + 2))) = 7/5, so a(4)=5.
For n=5, 1/(2 - 3/(3 - 4/(4 - 5/(5 + 2)))) = 41/13, so a(5)=13.
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PROG
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(Python)
from math import gcd, factorial
def A369797(n): return (a:=3*n-2)//gcd(a, a*sum(factorial(k) for k in range(n-2))+n*factorial(n-2)>>1) # Chai Wah Wu, Feb 26 2024
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CROSSREFS
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KEYWORD
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nonn,changed
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AUTHOR
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STATUS
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approved
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