A296222 Decimal expansion of the limiting ratio of terms in A296221.
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
Examples
A296221(n)/A296221(n-1) -> 3.651119422238034...
Programs
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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 *)
Comments