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, 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

Links

Table of n, a(n) for n=1..36.

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

Cf. A077624-A077635.

Equals 2*A017913(n) for n > 1.

Sequence in context: A331861 A032641 A293555 * A338122 A169873 A363788

Adjacent sequences: A077623 A077624 A077625 * A077627 A077628 A077629

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