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A296006 Decimal expansion of the limiting ratio of terms in A296005. 3
3, 1, 1, 4, 9, 8, 6, 4, 4, 7, 3, 9, 0, 3, 0, 2, 2, 4, 0, 2, 1, 1, 6, 2, 7, 0, 8, 7, 5, 5, 5, 4, 0, 3, 2, 8, 8, 3, 6, 0, 0, 9, 2, 9, 4, 5, 6, 0, 5, 9, 4, 2, 0, 4, 1, 3, 8, 8, 0, 8, 6, 4, 2, 5, 5, 2, 0, 9, 6, 6, 0, 7, 0, 5, 7, 3, 1, 7, 7, 4, 7, 9, 9, 6, 6, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A296005(n)/A296005(n-1)) -> 3.114986447390302...

See A296000 for a guide to related sequences and limiting ratios.

LINKS

Table of n, a(n) for n=1..86.

MATHEMATICA

mex[list_] := NestWhile[# + 1 &, 1, MemberQ[list, #] &];

a[0] = 2; a[1] = 3; b[0] = 1;

a[n_] := a[n] = Sum[a[k]*b[n - k - 1], {k, 0, n - 1}];

b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]];

Table[a[n], {n, 0, 100}];  (* A296005 *)

t = N[Table[a[n]/a[n - 1], {n, 1, 500, 100}], 200]

Take[RealDigits[Last[t], 10][[1]], 100]  (* A296006 *)

CROSSREFS

Cf. A296000, A296005.

Sequence in context: A263950 A160870 A025255 * A245397 A294316 A294761

Adjacent sequences:  A296003 A296004 A296005 * A296007 A296008 A296009

KEYWORD

nonn,easy,cons

AUTHOR

Clark Kimberling, Dec 07 2017

STATUS

approved

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Last modified May 25 03:50 EDT 2019. Contains 323539 sequences. (Running on oeis4.)