A251792 Decimal expansion of a constant related to A251702.

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, 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, 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

Offset: 1

Author

Vaclav Kotesovec and Jon E. Schoenfield, Dec 09 2014

Keywords

• nonn
• cons

Examples

			1.1546796279605837888382808629570944052320556413000593142798453022385779...
		

Crossrefs

Cf. A086714, A251702.

Programs

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

Mathematica

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 *)

Formula

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