A077627 Largest term in periodic part of continued fraction expansion of square root of -1+3^n.
2, 4, 10, 16, 30, 52, 92, 160, 280, 484, 840, 1456, 2524, 4372, 7574, 13120, 22726, 39364, 68182, 118096, 204550, 354292, 613654, 1062880, 1840964, 3188644, 5522896, 9565936, 16568690, 28697812, 49706070, 86093440, 149118214, 258280324, 447354646, 774840976, 1342063940
Offset: 1
Keywords
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..57
Programs
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Mathematica
Table[Max[Last[ContinuedFraction[Sqrt[ -1+3^u]]]], {u, 1, 32}]
Formula
a(2*m) = 2*(3^m-1); in general a(n) is close to 2*(3^(n/2)-1) and for any n, 0 <= a(n) - 2*(3^(n/2)-1) < 2. Conjecture: a(n)=ceiling(2*(3^(n/2)-1)) except for n=3, 9, 27 and all powers of 3, in this case a(n)=1+ceiling(2*(3^(n/2)-1)). - Benoit Cloitre, Nov 24 2002
Extensions
a(31)-a(37) from Chai Wah Wu, Oct 01 2019