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A077626
Largest term in periodic part of continued fraction expansion of square root of 1+3^n or 0 if 1+3^n is square.
0
0, 6, 10, 18, 30, 54, 92, 162, 280, 486, 840, 1458, 2524, 4374, 7574, 13122, 22726, 39366, 68182, 118098, 204550, 354294, 613654, 1062882, 1840964, 3188646, 5522896, 9565938, 16568690, 28697814, 49706070, 86093442, 149118214, 258280326, 447354646, 774840978
OFFSET
1,2
COMMENTS
a(n) = 0 iff n = 1, as a consequence of Catalan's conjecture or Mihăilescu's theorem. - Bernard Schott, Apr 25 2022
MATHEMATICA
Table[Max[Last[ContinuedFraction[Sqrt[1+3^u]]]], {u, 1, 32}]
PROG
(PARI) a(n) = if (n==1, 0, 2*sqrtint(3^n)); \\ Michel Marcus, Apr 20 2022
CROSSREFS
Equals 2*A017913(n) for n > 1.
Sequence in context: A331861 A032641 A293555 * A338122 A169873 A363788
KEYWORD
nonn
AUTHOR
Labos Elemer, Nov 13 2002
EXTENSIONS
a(1) changed and definition clarified by Chai Wah Wu, Sep 18 2021
a(31)-a(36) from Chai Wah Wu, Apr 20 2022
STATUS
approved