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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
OFFSET
1,1
COMMENTS
A296005(n)/A296005(n-1)) -> 3.114986447390302...
See A296000 for a guide to related sequences and limiting ratios.
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
Sequence in context: A376335 A342447 A025255 * A245397 A346792 A294316
KEYWORD
nonn,easy,cons
AUTHOR
Clark Kimberling, Dec 07 2017
STATUS
approved