A258112 - OEIS

%I #7 May 20 2015 17:39:05

%S 1,7,9,7,8,7,8,4,9,0,0,0,9,1,6,0,4,8,1,3,5,5,9,5,0,8,8,3,7,0,3,1,3,5,

%T 2,1,6,1,7,9,3,6,6,5,2,6,5,0,1,9,5,2,5,3,6,8,5,5,2,3,6,2,5,4,2,7,4,5,

%U 5,8,4,1,3,2,4,6,3,6,0,7,4,1,7,3,9,2,7,8,8,0,5,6,9,3,2,4,0,9,5,6,6,8,5,9,9

%N Decimal expansion of a constant related to A001056.

%F Equals limit n->infinity (A001056(n))^((2/(1+sqrt(5)))^n).

%e 1.7978784900091604813559508837031352161793665265019525368552362542745...

%t A001056 = RecurrenceTable[{a[0]==1, a[1]==N[3, 200], a[n] == a[n-1]*a[n-2]+1}, a[n], {n, 1, 30}]; Do[Print[N[Exp[c2]/.Solve[Table[Log[A001056[[n]]] == c1*((1-Sqrt[5])/2)^n + c2*((1+Sqrt[5])/2)^n, {n, k, k+1}]], 120][[1]]], {k, Length[A001056]-2, Length[A001056]-1}];

%Y Cf. A001056, A076949, A258113.

%K nonn,cons

%O 1,2

%A _Vaclav Kotesovec_, May 20 2015