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

1,3

Links

Table of n, a(n) for n=1..105.

Formula

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

Example

1.1546796279605837888382808629570944052320556413000593142798453022385779...

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 *)

Prog

(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

Crossrefs

Cf. A086714, A251702.

Sequence in context: A153451 A190143 A089687 * A159894 A011502 A347185

Adjacent sequences: A251789 A251790 A251791 * A251793 A251794 A251795

Keyword

nonn,cons

Author

Vaclav Kotesovec and Jon E. Schoenfield, Dec 09 2014

Status

approved