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A239502
(Round(q^prime(n)) - 1)/prime(n), where q is the tribonacci constant (A058265).
5
4, 10, 74, 212, 1856, 5618, 53114, 1630932, 5161442, 167427844, 1729192432, 5577731626, 58401766802, 2005139696964, 69737304018266, 228184540445268, 8043367476888770, 86866463049858250, 285815985033409648, 10225367934387562098, 111384745483589787826
OFFSET
3,1
COMMENTS
For n>=3, round(q^prime(n)) == 1 (mod 2*prime(n)). Proof in Shevelev link. In particular, all terms are even.
LINKS
S. Litsyn and V. Shevelev, Irrational Factors Satisfying the Little Fermat Theorem, International Journal of Number Theory, vol.1, no.4 (2005), 499-512.
V. Shevelev, A property of n-bonacci constant, Seqfan (Mar 23 2014)
Eric Weisstein's World of Mathematics, Tribonacci Constant
EXAMPLE
For n=3, q^5 = 21.049..., so a(3) = (21 - 1)/5 = 4.
KEYWORD
nonn
AUTHOR
STATUS
approved