%I #14 Sep 08 2022 08:46:10

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

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

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

%N Decimal expansion of a constant related to A251702.

%F Equals lim_{n->infinity} A251702(n)^(1/3^n).

%e 1.1546796279605837888382808629570944052320556413000593142798453022385779...

%t exact = 20; terms = 200; b = ConstantArray[0, terms]; b[[1]] = N[Log[5], 100]; Do[b[[n]] = b[[n - 1]] + If[n > exact, b[[n - 1]], Log[Exp[b[[n - 1]]] - 1]] + If[n > exact, b[[n - 1]], Log[Exp[b[[n - 1]]] - 2]] - Log[6], {n, 2, terms}]; Do[Print[Exp[b[[n]]/3^n]], {n, 1, Length[b]}] (* after _Jon E. Schoenfield_ *)

%o (Magma) nMax:=160; nExactMax:=20; DP:=100; R:=RealField(DP); SetDefaultRealField(R); logA:=[Log(5.0)]; for n in [2..nMax] do logAprev:=logA[n-1]; if n le nExactMax then Aprev:=Exp(logAprev); logA[n]:=logAprev + Log(Aprev-1) + Log(Aprev-2) - Log(6); else logA[n]:=3*logAprev - Log(6); end if; t:=Exp((1/3^n)*logA[n]); n, ChangePrecision(t,72); end for; // _Jon E. Schoenfield_, Dec 09 2014

%Y Cf. A086714, A251702.

%K nonn,cons

%O 1,3

%A _Vaclav Kotesovec_ and _Jon E. Schoenfield_, Dec 09 2014