Voozh

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

(list; graph; refs; listen; history; text; internal format)

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