A296228 Decimal expansion of the limiting ratio of terms in A296227.
4, 3, 0, 3, 3, 9, 6, 3, 0, 3, 1, 3, 3, 0, 4, 0, 0, 6, 6, 1, 7, 5, 7, 5, 8, 0, 9, 6, 3, 3, 2, 1, 4, 8, 7, 1, 3, 8, 8, 6, 4, 4, 1, 0, 2, 0, 2, 7, 2, 6, 5, 2, 3, 4, 1, 5, 1, 6, 0, 7, 0, 7, 8, 7, 6, 6, 8, 3, 5, 8, 2, 3, 1, 4, 6, 6, 8, 7, 0, 5, 0, 2, 3, 8, 2, 4
Offset: 1
Examples
4.3033963031...
Programs
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Mathematica
mex[list_] := NestWhile[# + 1 &, 1, MemberQ[list, #] &]; a[0] = 1; a[1] = 2; b[0] = 3; a[n_] := a[n] = - 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, 200}] (* A296227 *) Table[b[n], {n, 0, 20}] N[Table[a[n]/a[n - 1], {n, 1, 200, 10}], 200]; RealDigits[Last[t], 10][[1]] (* A296228 *)
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