|
%I #21 Apr 25 2022 11:27:31
%S 0,6,10,18,30,54,92,162,280,486,840,1458,2524,4374,7574,13122,22726,
%T 39366,68182,118098,204550,354294,613654,1062882,1840964,3188646,
%U 5522896,9565938,16568690,28697814,49706070,86093442,149118214,258280326,447354646,774840978
%N Largest term in periodic part of continued fraction expansion of square root of 1+3^n or 0 if 1+3^n is square.
%C a(n) = 0 iff n = 1, as a consequence of Catalan's conjecture or Mihăilescu's theorem. - _Bernard Schott_, Apr 25 2022
%t Table[Max[Last[ContinuedFraction[Sqrt[1+3^u]]]], {u, 1, 32}]
%o (PARI) a(n) = if (n==1, 0, 2*sqrtint(3^n)); \\ _Michel Marcus_, Apr 20 2022
%Y Cf. A077624-A077635.
%Y Equals 2*A017913(n) for n > 1.
%K nonn
%O 1,2
%A _Labos Elemer_, Nov 13 2002
%E a(1) changed and definition clarified by _Chai Wah Wu_, Sep 18 2021
%E a(31)-a(36) from _Chai Wah Wu_, Apr 20 2022
|
