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Length of the smallest prefix of the continued fraction expansion for Pi that includes each of 1..n.
1

%I #6 Aug 05 2024 14:54:42

%S 4,9,9,30,40,40,40,44,130,130,276,276,276,276,276,276,647,647,647,647,

%T 647,647,647,647,791,791,791,791,791,791,878,878,878,878,1008,1008,

%U 1008,3041,3041,3041,3041,3041,3041,3041,3041,3200,3200,3200,3200,3200,3200

%N Length of the smallest prefix of the continued fraction expansion for Pi that includes each of 1..n.

%F a(n) = max(A032523(n), a(n-1)) for n > 1. - _Andrew Howroyd_, Aug 05 2024

%t f[n_] := Block[{k = 1}, While[ StringPosition[ ToString[ Union[ ContinuedFraction[Pi, k]]], StringDrop[ ToString[ Table[i, {i, n}]], -1]] == {}, k++ ]; k]; Table[ f[n], {n, 1, 51}]

%Y Cf. A001203, A032523.

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Jan 26 2004

%E Name clarified by _Andrew Howroyd_, Aug 05 2024