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A296222
Decimal expansion of the limiting ratio of terms in A296221.
2
3, 6, 5, 1, 1, 1, 9, 4, 2, 2, 2, 3, 8, 0, 3, 4, 7, 5, 8, 6, 4, 0, 5, 0, 0, 5, 1, 9, 7, 9, 2, 7, 3, 1, 3, 8, 8, 9, 8, 5, 2, 8, 9, 7, 5, 8, 3, 6, 3, 3, 5, 4, 0, 1, 5, 3, 1, 6, 7, 9, 4, 8, 7, 3, 9, 5, 9, 6, 9, 0, 3, 2, 6, 0, 2, 0, 8, 4, 2, 4, 0, 5, 4, 2, 8, 9
OFFSET
1,1
COMMENTS
See A296000 for a guide to related sequences and limiting ratios.
EXAMPLE
A296221(n)/A296221(n-1)) -> 3.651119422238034...
MATHEMATICA
mex[list_] := NestWhile[# + 1 &, 1, MemberQ[list, #] &];
a[0] = 1; a[1] = 3; b[0] = 2;
a[n_] := a[n] = Sum[a[k]*b[n - k - 1], {k, 0, n - 1}] + 1;
b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]];
u = Table[a[n], {n, 0, 200}]; (* A296221 *)
Table[b[n], {n, 0, 20}]
N[Table[a[n]/a[n - 1], {n, 1, 200, 10}], 200];
RealDigits[Last[t], 10][[1]] (* A296222 *)
CROSSREFS
KEYWORD
nonn,easy,cons
AUTHOR
Clark Kimberling, Dec 09 2017
STATUS
approved